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LIBRARY- OF CONGRESS. 



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UNITED STATES OF AMERICA. 









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Dudley Observatory, at Albany, N.Y. 



POPULAR ASTRONOMY, 



CONCISE ELEMENTARY TREATISE 



ON THE 



SUN, PLAiNETS, SATELLITES AND COMETS. 



BY 

/ 



V 



0. M. MITCHEL, LL.D., 

DIRECTOR OF THE CINCINNATI AND DUDLEY OBSERVATORIES. 



y 



NEW YORK: 
PIIINNEY, BLAKEMAN & MASON, 

No. 61 W ,VI,K EE STREET, 

I 8 6 . 



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QP 



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Entered, according to Act of Congress, in the year 1S60, by 

0. M. MITCIIEL, 

In the Clerk's Office of the District Court for the Southern District of New York. 



8TEBE0TYPED JiY FEINTED BY 

SMITH & McDOUGAL, J. D. BEDFORD & CO 

82 & 84 Beekman-st. , N. Y. 1 15 & 117 Franklin St. 



& 



A PREFACE. 

/V 

s 

A) 

The author has no other apology to present for offer- 
ing to the public the following work on " Popular 
Astronomy" than the marked favor with which his 
" Planetary and Stellar Worlds" has been received, both 
in this country and in Europe. 

The science of Astronomy is so rapidly progressive 
that to keep the public advised of its advances new 
works are required almost every year. This may be 
offered as an additional reason for the present publica- 
tion. 

In the preparation of the work I have availed myself 
of so many sources of information that it would be quite 
impossible for me to specify the authors or the volumes 
to which I am indebted. The plan and the cast is all 
my own. I have endeavored to follow the path of real 
discovery, and in every instance to present the facts and 
phenomena so as to afford to the reader and student an 
opportunity to exercise his own genius in their discussion 



IV PREFACE. 

and resolution, before offering the explanation reached by 
ancient or modern science. It is hoped that this method 
of treating the subject which is new, (so far as I know,) 
may avail in exciting a greater interest in the examination 
of those great problems of the universe whose successful 
solution constitutes the chief honor of human genius. 

In a few instances I have ventured to present the 
results of my own observations, and have occupied a 
short space in exhibiting a sketch of new methods and 
new instruments, which have been introduced into the 
observatories at Cincinnati and at Albany. 

Dudley Observatory, January, 1860. 



CONTENTS 



CHAPTER I. 

THE SUN, THE CENTRAL ORB OP THE PLANETARY SYSTEM. 

PAGE 

Discoveries of the Ancients. — The Source of Light and Heat and Life. — The 
Sun's apparent Motion. — Length of the Year. — The Sun's apparent Path 
among the Fixed Stars, a Circle. — His apparent Motion not Uniform. — The 
Explanation of Hipparchus. — Solar Eclipses. — Their Prediction. 

Discoveries of tiie Moderns. — The Sun's Distance. — His Horizontal Paral- 
lax Importance of this Element. — Measured by the Transit of Venus. — 

The Sun's real Magnitude, and Micrometrical Measure of his Diameter. — 
The Physical Constitution of the Sun. — Solar Spots. — Their Periodicity. — 
Hypotheses and Speculations 13 

CHAPTER II. 

MERCURY, THE FTRST PLANET IN THE ORDER OF DISTANCE 
FROM THE SUN. 

Its Early Discovery. — Difficult to be distinguished from the Stars. — Elonga- 
tions. — Motion Direct and Retrograde. — Sometimes Stationary. — Nature of 
the Orbit. — Variation in the Elongation Explained. — The Nodes. — Transit of 
Mercury. — Inclination of Mercury's Orbit.— Mean Distance from the Sun. — 
Conjunctions. — Phases.— Diameter and Volume 45 

CHAPTER III. 

VENUS, TIIE SECOND PLANET IN THE ORDER OF DISTANCE FROM 
THE SUN. 

The First Planet Discovered. — Mode of its Discovery.— Her Elongations.- • 
Morning and Evening Star. — A Sattellite of the Sun. — Her superior and In- 
ferior Conjunctions. — Her Stations. — Direct and Retrograde Motions. — These 
Phenomena indicate a Motion of the Earth. — Transits of Venus. — Inclina- 
tion of the Orbit of Venus to the Ecliptic. — Her Nodes.— Intervals of her 
Transits. — Knowledge of the Ancients. — Phases oi Venus. — Her Elongations 
Unequal. — No Sattellite yet Discovered.— Sun's Light and Heat at Venus.— 
Her Atmosphere ; 62 

CHAPTER IV. 

THE EARTH AND ITS SATTELLITE; TIIE THIRD PLANET IN THE 
ORDER OF DISTANCE FROM TIIE SUN. 

The Earth the apparent Center of Motion.— To all the Senses it is at Rent— 
The Center of the Motions of the Sun and Moon.— Explanation o( the Ac- 
celeration of the Orbitual Motion of the Bun and Moon. — Ptolemy's Epicy- 
cles. — The Explanation of Copernicus. — The Sun the Center of Planetary 
Motion.— The Earth One of the Planets.— Objections to this Hypothesis.— 
The Answer. — System of Jupiter discovered by the Teleseope. — The Old Sys- 
tem superseded by the New. — The Figure and Magnitude of the Earth — 
How determined.— The Earth's Motions. — Rotation and Revolution.- A 
Unit Of Time furnished by the Earth's Period of Rotation.— Earth's Orbit- 
ual Motion.— Vernal Equinox.— Perihelion o( Earth's Orbit.— its Period of 
Revolution.— Solar and Sidereal Time. 

Tub Moon.— Revolution in her Orbit.— Her Phases.— Eccentricity of her Or- 
bit—Revolution of her Apogee.— Inclination of her Orbit— Moon's Paral- 
lax and Distance.— llor Physical Constitution.— Center o( Gravity and Cen- 
ter of Figure ." $i 



VI CONTENTS. 



CHAPTER Y. 

MARS, THE FOURTH PLANET IN THE ORDER OF DISTANCE FROM 
THE SUN. 

PAGB 

Phenomena of Mars difficult to explain with the Earth as the Center of Mo- 
tion. — Copernican system applied. — Epicycle of Mars. — Better Instruments 
and more accurate Observations. — Tycho and Kepler. — Kepler's method of 
Investigation. — Circles and Epicycles exhausted. — The Ellipse.— Its Proper- 
ties. — The Orbit of Mars an Ellipse. — Kepler's Laws. — Elliptical Orbits of 
the Planets. — The Elements of the Planetary Orbits explained — How these 
Elements are obtained. — Kepler's third Law. — Value of this Law. — The Phys- 
ical Aspect of Mars. — Snow Zones. — Rotation of the Planet. — Diameter and 
Volume. — Speculation as to its Climate and Color. 102 



CHAPTER VI. 

THE ASTEROIDS: A GROUP OF SMALL PLANETS, THE FIFTH IN THE 
ORDER OF DISTANCE FROM THE SUN. 

The Interplanetary Spaces. — Kepler's Speculations.— Great Interval between 
Mars and Jupiter. — Bode's Empirical Law. — Conviction that a Planet exist- 
ed between Mars and Jupiter. — Congress of Astronomers. — An Association 
Organized to Search for the Planet.— Discovery of Ceres. — Lost in the Solar 
Beams. — Rediscovered by Gauss. — The New Order Disturbed by the Dis- 
covery of Pallas. — Olber's Hypothesis. — Discovery of Juno and Vesta — The 
Search Ceases. — Renewed in 1845. — Many Asteroids discovered. — Their Mag- 
nitude, Size, and probable N umber „ 125 



CHAPTER VII. 

JUPITER, ATTENDED BY FOUR. MOONS, THE SIXTH PLANET LN THE 
ORDER OF DISTANCE FROM THE SUN. 

Arc of Retrogradation.— Stationary Point.— Distance of the Planet Determined. 
— Periodic" Time. — Synodical Revolution gives the Sidereal. — Surface of Ju- 
piter as given by the Telescope — Period of Rotation— Diameter.— Volume. 
— Mean Distance. — Amount of Light and Heat. — Figure of Jupiter. — Equa- 
torial and Polar Diameters. — Discovery of the Four Moons by Galileo. — Ef- 
fect on the Copernican Theory —Jupiter's Nocturnal Heavens. 

The Sattellitesof Jupiter. — How Discovered. — Their Magnitude. — Form of 
their Orbits. — Period of Revolution.— Eclipses.— Transits. — Occultations. — 
Velocity of Light Discovered. — Terrestrial Longitude. — Rotation of these 
Moons on an Axis . 134 



CHAPTER VIII. 

SATURN, THE SEVENTH PLANET IN THE ORDER OF DISTANCE FROM 
THE SUN, SURROUNDED BY CONCENTRIC RINGS, AKD ATTENDED 
BY EIGHT SATELLITES. 

The most Distant of the Old Planets.— Its Light Faint, but Steady.— Synodi- 
cal Revolution.— The Sidereal Revolution.— Advances in Telescopic Discov- 
ery.— Galileo announces Saturn to be Triple.— Hnygens Discovers the Ring. 
— Division of the Ring into Two. — Cassini announces the Outer Ring the 
Brighter.— Multiple Division— Shadow of the Planet on the Ring— Belts 
and Spots.— Period of Rotation of the Planet and the Ring.— Disappearance- 
of the Ring Explained. — The Dusky Ring. 

Satellites of Saturn. — By whom Discovered. — Eight in Number. — Their 
Distances and Periods.— Saturn's Orbit the Boundary of the Planetary Sys- 
tem, as known to the Ancients 156 



CONTENTS. Vll 

CHAPTER IX. 

THE LAWS OF MOTION AND GRAVITATION. 

PAGE 

The Demands of Formal Astronomy.— Those of Physical Astronomy.— Syn- 
opsis of the Discoveries already made. — Questions remaining to be Answered. 
— Inquiry into Causes. — The Laws of Motion demanded. — Rectilineal Mo- 
tion. — Falling Bodies. — Law of Descent. — Motion of Projectiles.— Curvilin- 
ear Motion. — First Law of Motion. — Second Law of Motion. — Momentum 
of Moving Bodies. — Motion on an Inclined Plane. — The Centrifugal Force. 
— Central Attraction. — Gravitation. — Laws of Motion applied to the Planets. 
— Questions Propounded in Physical. Astronomy. — Newton's Order of Inves- 
tigation. — His assumed Law of Gravitation. — Outline of his Demonstration. 
— Its Importance aud Consequences. — The Law of Gravitation embraces all 
the Planets and their Satellites.— Gravitation Resides in every Particle of 
Matter 166 



CHAPTER X. 

THE LAWS OF MOTION AND GRAVITATION APPLIED TO A SYSTEM OF 
THREE REVOLVING BODIES. 

A System of two Bodies.— Quantities Required in its Investigation.— Five in 
Number. — Sun and Earth. — Sun, Earth and Moon, as Systems of Three 
Bodies. — The Sun supposed Stationary.— Changed Figure of the Moon's Or- 
bit. — Sun Revolving Changes the Position of the Moon's Orbit. — Solar Orbit 
Elliptical. — Effects Resulting from the Inclination of the Moon's Orbit. — 
Moon's Motion above and below the Plane of the Ecliptic. — Revolution of 
the Line of Nodes. — Sun, Earth and Planet, as the Three Bodies. — Perturba- 
tions Destroy the Rigor of Kepler's Laws. — Complexity thus Introduced. — 
Infinitesimal Analysis. — Difference between Geometrical and Analytical 
Reasoning 194 



CHAPTER XI. 

INSTRUMENTAL ASTRONOMY. 

Method for Obtaining the Mass of the Sun.— For getting the Mass of a Planet 
with aSatellite. — For weighing a Planet having no Satellite. — For weighing 
the Satellites. — Planetary Distances to be Measured. — Intervals between 
Primaries and their Satellites to be Obtained. — Intensity and Direction of 
the Impulsive Forces to be Determined — -These Problems all Demand In- 
strumental Measures.— Differential Places.— Absolute Places.— The Transit 
Instrument.— Adjustments. — Instrumental Errors — Corrections Due to Va- 
rious Causes. — American Method of Transits. — Meridian Circle. — The De- 
clinometer '210 



CHAPTER XII. 

URANUS, THE EIGHTH PLANET IN THE ORDER OF DISTANCE FROM 
THE SUN. 

Accidentally Discovered by Sir William llerseliell. — Announced as a Comet. 
— Its Orbit proved it tu be a Superior Planet. — The Kletnents of its Orbit 
Obtained. — Are of Uetrogradatiou. — Period of Revolution. — Figure of the 
Planet.— Inclination nf its Orbit.— Six Satellites Announced by the Elder 

llerseliell. — Pour of these now Reoogntied, — Their Orbital Planes and 1M- 

rections of Revolution Anomalous. — Efforts made to Tabulate the Plaoes of 

Uranus Unsuccessful, — This Leads to the Discovery of a New Exterior 
Planet , Mfl 



Vlll CONTENTS. 



CHAPTER XIII. 

NEPTUNE, THE NINTH AND LAST KNOWN PLANET IN THE ORDER OF 
DISTANCE FROM THE SUN. 

PAGE 
Uranus Discovered by Accident. — Ceres by Research with the Telescope. — 
Rediscovered by Mathematical Computation. — The Perturbations of Uranus. 
— Not due to any known Cause. — Assumed to Arise from an Exterior Planet. 
— Nature of the Examination to find the Unknown Planet.— Undertaken at 
the 6ame time by two Computers. — Computation Assigns a Place to the Un- 
known Planet. — Discovered by the Telescope. — Discoveries Resulting. — A 
Satellite Detected.— The Mass of Neptune thus Determined.— Neptune's 
Orbit the Circumscribing Boundary of the Planetary System 266 



CHAPTER XIV. 

THE COMETS. 

Objects of Dread in the Early Ages. — Comets Obey the Law of Gravitation 
and Revolve in some one of the Conic Sections. — Characteristics of these 
Curves.— Comet of 1680 Studied by Newton. — Comet of 16S2 named " Hal- 
ley's Comet." — Its History. — Its Return Predicted. — Perihelion Passage 
Computed. — Passes its Perihelion 13th April, 1759 — Elements of its Orbit. 
— Physical Constitution. — Nucleus. — Envelopes. — Tail. — Intense Heat Suf- 
fered' by some Comets in Perihelio. — Dissipation of the Cometic Matter. — 
Encke's Comet. — A Resisting Medium. — Deductions from Observation. — 
Biela's Comet.— Divided.— Number of Comets 



CHAPTER XV. 

THE SUN AND PLANETS AS PONDERABLE BODIES. 

General Circumstances of the System. — The Sun. — His Diameter and Mass. — 
Gravity at the Surface. — Mercury. — His Mass and Perturbations. — Venus as 
a Ponderable Body. — Long Equation of Venus and the Earth. — The Earth 
and Moon as Heavy Bodies. — Figure and Mass of the Earth. — Precession. — 
Aberration. — Nutation.— Mars. — His Mass and Density. — Gravity at His Sur- 
face. — The Asteroids. — Jupiter's System. — Saturn. — His Moons and Rings as 
Ponderable Bodies. — Uranus. — Neptune. — Stability of the whole System... . 



CHAPTER XVI. 



THE NEBULAR HYPOTHESIS. 



The Arrangement of the Solar System.— The Phenomena for which Gravitation 
is Responsible. — The Phenomena Remaining to be Accounted for. — Nebu- 
lous Matter as found in Comets. — Nebulous Matter Possibly in the Heavens. 
— The Entire Solar System once a Globe of Nebulous Matter. — Motion of 
Rotation. — Radiation of Heat. — Condensation and its Effects. — Rings disen- 
gaged from the Equator of the Revolving Mass. — Formation of Planets and 
of Satellites 349 



INTRODUCTION. 



The great dome of the heavens, filled with a countless 
multitude of stars, is beyond a doubt the most amazing 
spectacle revealed by the sense of sight. It has excited 
the admiration and curiosity of mankind in all ages of 
the world. The study of the stars is therefore coeval 
with our race, and hence we find many discoveries in the 
heavens of whose origin neither history nor tradition can 
give any account. The science of Astronomy, embracing, 
as it does, all the phenomena of the celestial orbs, has 
furnished in all ages the grandest problems for the exer- 
cise of human genius. In the primitive ages its ad- 
vances were slow, but by patient watching, and by dili- 
gent and faithful records transmitted to posterity from 
generation to generation, the mysteries which fill the 
heavens were one by one mastered, until at length, in 
our own age, there remains no phenomenon of motion 
unexplained, while the distances, magnitudes, masses, 
reciprocal influences, and physical constitution of the 
celestial orbs have been approximately revealed. In a. 
former volume an attempt was made to trace the career 
of discovery among the stars, and to exhibit the successive 
steps by which the genius of man finally reached the so- 
lution of the great problem of the universe. 

The performance of that task did not permit the special 
study of any one object, except so far as ii was required 
in the march of the general investigation. It is our 



X INTRODUCTION. 

object now to execute what was then promised, and to 
examine in detail the various bodies which are allied to 
the sun, constituting (as we shall find) a delicately or- 
ganized system of revolving worlds, a complex mechanical 
structure, whose stability has challenged the admiration 
of all thinking minds, and whose organization has fur- 
nished the most profound themes of human investiga- 
tion. 

The plan adopted will lead us to present clearly all the 
facts and phenomena resulting from observation; with 
these facts the student may exercise his own genius in 
attempting to account for the phenomena, before proceed- 
ing to accept the explanation laid down in the text. 

To aid the memory and to present a systematic investi- 
gation, we shall adopt the simple order of distance from 
the solar orb, commencing with that grand central lumi- 
nary, and proceeding outward from planet to planet, 
until we shall develop all the phenomena employed in the 
discovery of the great law of universal gravitation. With 
a knowledge of this law the worlds already examined 
cease to be isolated, and arrange themselves under the 
empire of gravitation into a complex system, the delicate 
relations of whose parts, leads to new discovery and to 
the final perfection of the system of solar satellites. 

Having closed our investigation of the planets and their 
tributary worlds, we shall render an account of those 
anomalous bodies called comets, which, by the sudden- 
ness of their appearance, their rapid and eccentric mo- 
tions, and the brilliant trains of light which sometimes 
attend them, have excited universal interest, not unat- 
tended with alarm in all ages of the world. 

Before passing to the execution of this plan, we must 
examine, to some extent, the phenomena of the nocturnal 



INTRODUCTION. XI 

heavens, as the stars furnish the fixed points to which 
all moving bodies are referred. 

To the eye the heavens rise as a mighty dome, a vast 
hollow hemisphere, on whose internal surface the glitter- 
ing stars remain forever fixed. In case we watch through 
an entire night, we find the groupings of stars slowly 
rising from the east, gradually reaching their culmina- 
tion, and then gently sinking in the west. A more at- 
tentive examination enables the eye to detect some of 
these groups of stars toward the north which ever remain 
visible, rising, culminating, and descending, but never 
sinking below the horizon. Every star in this diurnai 
revolution, as it is called, is found to describe a circle, 
precisely as if the concave heavens were a hollow sphere 
to which the stars were attached, and that this hollow 
globe, were made to revolve about a fixed axis, passing 
through its center. Indeed, we find by attentively watch- 
ing, that this hypothesis of a spherical heavens accounts 
for all the phenomena already presented. As the stars are 
situated nearer to the extremity of the axis of revolution 
the circles they describe grow smaller and smaller, until, 
finally, we find one star which remains fixed, and this one 
must be at the point where the axis of the heavens 
pierces the celestial sphere. This is called the north 
star ; and the point in which the axis pierces the heavens 
is called the north pote. The opposite point is called 
the south pole. 

Only one half of the celestial sphere is visible at one 
time above the horizon, but this spherical surface ex- 
tends beneath the horizon, and forms a complete sphere, 
encompassing us on all sides, while its center seems to be 
occupied by the earth. It is true that, in the day-time, 
the stars fade from the sight in the solar blaze, but they 



Xll INTRODUCTION. 

are not lost ; they still fill the heavens, as we shall see 
hereafter, and the starry sphere sweeps unbroken entirely 
round the earth. 

These great truths, the diurnal revolution of the heav- 
ens, its spherical form, the central position of the earth, 
the north polar star, the axis of the heavens, the circles 
described by the stars, were among the discoveries of 
primitive antiquity, and are matters of the most simple 
observation. 

The spherical form of the heavens was soon imitated, 
and the artificial globe became one of the first astronom- 
ical instruments. On this artificial globe certain lines 
were drawn to imitate those described in the heavens by 
the celestial orbs, and as these lines must henceforth 
form a part of our language we proceed to give the fol- 
lowing Definitions : — 

A great circle is one whose plane passes through the 
center of the sphere. 

A small circle is one whose plane does not pass through 
the center of the sphere. 

The axis of the heavens is an imaginary line passing 
through the center of the earth, and about which the 
heavens appear to revolve once in twenty-four hours. 

A meridian is a great circle passing through the 
highest point of the celestial sphere (called the zenith) 
and the axis of the heavens. 

The equator or equinoctial is a great circle, perpen- 
dicular to the axis of the heavens, and half-way between 
the north and south polar points. 

These important lines have been employed from the 
earliest ages in the study of the heavenly bodies, and 
having thoroughly mastered their meaning and position 
we are prepared to examine any changes of location which 



INTRODUCTION. Xlll 

may be discovered among the vast multitude of shining 
bodies which go to fill up the concave of the celestial 
sphere. 

We shall proceed, then, without further delay, to the 
execution of the plan already laid down. 



CHAPTER I . 

THE SUN, THE CENTRAL ORB OF THE PLANETARY 
SYSTEM. 

DISCOVERIES OF THE ANCIENTS— The Source of Life and Light and 
Heat. — The Sun's Motion among the Stars. — His Orbit circular. — 
Length of the Year.— Inequality of the Sun's Motion. — Explained 
by Hipparchus.— Solar Eclipses. — Their First Prediction. 

DISCOVERIES OF THE MODERNS.— The Sun's Distance.— His Horizontal 
Parallax. — Importance of this Element. — Measured by the Transit of 
Venus. — The Sun's actual Diameter and real Magnitude. — His Rota- 
tion. — The Solar Spots. — Their Periodicity. — Speculations as to the 
Physical Constitution of the Sun. 

The sun is beyond comparison the grandest of all the 
celestial orbs, of -which we have any positive knowledge. 
The inexhaustible source of the heat which warms and 
vivifies the earth, and the origin of a perpetual flood of 
light, which, flying with incredible velocity in all direc- 
tions, illumines the planets and their satellites, lights up 
the eccentric comets, and penetrates even to the region 
of the fixed stars ; it is not surprising that in the early 
ages of the world, this mighty orb should have been re- 
garded as the visible emblem of the Omnipotent, and as 
such should have received divine honors. 

On the approach of the sun to the horizon in the early 
dawn, his coming is announced by the gray eastern twi- 
light, before whose gradual increase the brightest stars 
and even the planets fade and disappear. The coming 
splendor grows and expands, rising higher and yet higher, 
until, as the first beam of sunlight darts on the world, not 
a star or planet remains visible in the whole heavens, and 



16 THE SUN. 

even the moon, under this flood of sunlight, shines only 
as a faint silver cloud. 

This magnificent spectacle of the sunrise, together 
with the equally imposing scenes which sometimes ac- 
company the setting sun, must have excited the curiosity 
of the very first inhabitants of the earth. This curiosity 
led to a more careful examination of the phenomena at- 
tending the rising and setting sun, when it was discovered 
that the point at which this great orb made his appear- 
ance was not fixed, but was slowly shifting on the horizon, 
the change being easily detected by the observation of a 
few days. Hence was discovered, in the primitive ages — 

The sun's apparent motion. — In case the sun is 
observed attentively from month to month it will be found 
that the point of sunrise on the horizon moves slowly, for 
a certain length of time, toward the south. While this 
motion continues, the sun, at noon, when culminating on 
the meridian, reaches each day a point less elevated above 
the horizon, and the diurnal arc or daily path described 
by the sun grows shorter and shorter. At length a 
limit is reached ; the point of sunrise ceases to advance 
toward the south, remaining stationary a day or two, 
and then slowly commences its return toward the north. 
This northern movement continues ; each day the sun 
mounts higher at his meridian passage, the diurnal arc 
above the horizon grows longer and longer, until, again, 
a northern limit is reached, beyond which the sun never 
passes. Here he becomes stationary for one or two days, 
and then commences his return toward the south. Thus 
does the sun appear to vibrate backward and forward be- 
tween his southern and northern limits, marking to man 
a period of the highest interest, for within its limits the 
spring, the summer, the autumn, and the \Dinter, have 



THE SUN. 17 

run their cycles, and by their union have wrought out 
the changes of the year. 

The length of this important period was, doubtless, 
first determined by counting the days which elapsed from 
the time when the sun rose behind some well-defined 
natural object in the horizon until his return in the same 
direction to the same point of rising. Of course, these 
changes in the sun's place were studied with profound 
attention. They were among the first celestial phenom- 
ena discovered, and among the first demanding explana- 
tion. The stars were found never to change their points 
of rising, culmination, and setting. Their diurnal arc 
remained forever the same, and the amount of time they 
remained above the horizon depended on their distance 
from the north polar point. 

Observation having thus revealed the fact that the sun 
was undoubtedly moving alternately north and south, a 
more critical research showed the equally important 
truth, that this great luminary was slowly shifting its 
place among the fixed stars. This was not so readily 
determined ; but by noting the brilliant stars which first 
appeared in the evening twilight, after sunset, it was 
soon discovered that these stars did not long remain vis- 
ible. Indeed, the whole starry heavens seemed, from 
night to night, to be plunging downward to overtake the 
setting sun, or rather, that the sun himself was mounting 
upward to meet the stars, and thus was discovered a solar 
motion in a direction opposed to the diurnal revolution 
of the heavens. 

From month to month the sun was soon to advance 
among the stars, and at the end of an entire year, after 
all the former changes of northern and southern motion 
had been accomplished, the sun was found to return to 



18 THE SUN. 

the same group of fixed stars from whence he set out ; 
and thus it became manifest that this revolution among 
the stars was identical in period with the changes from 
north to south, and hence these phenomena had, in all 
probability, a common origin. 

Here was the first great problem offered for solution 
to the old astronomers. The facts and phenomena were 
carefully studied, and the reader may now exercise his 
own power of thought in an effort to explain the facts 
recorded, before accepting the solution we are about to 
present. 

An examination of the points of rising, of culmination, 
and of setting, of the fixed stars, showed them to be ab- 
solutely invariable, and in case these glittering points 
could leave behind them, in their diurnal revolution, 
lines of silver light, sweeping upward from their point of 
rising to the meridian, and downward to the point of 
setting, these lines of light would be seen to be parallel 
circles. All the stars north of the equinoctial (in the 
region of the earth we inhabit) describe diurnal circles, 
of which more than one half is above the horizon, while 
all the stars south of the same line sweep round in circles, 
of which less than half lies above the same plane. Any 
star, precisely on the equinoctial, half way between the 
north and south poles, passes one half its revolution 
above and the other half below the horizon. 

These facts being carefully noted, it was seen that in 
case the sun, on any day of its annual journey, chanced 
to coincide with a fixed star, that for that day the sun 
and star would describe the same diurnal circle, and 
would remain above the horizon an equal length of time. 
Thus along the sun's path it became possible to select a 
number of stars over which the sun passed, and which 



THE SUN. 19 

would by their position mark his route in the heavens. 
To aid in this investigation, as well as for some other 
purposes, the ancients erected a vertical staff on a level 
plane, and then noted where the shadow of the top of the 
staff fell at noon each day throughout the year. This 
instrument was called a gnomon, and its use revealed 
many important facts in the solar motion, and detected 
others hitherto overlooked. If on the same day we note 
carefully the length of the shadow of the gnomon a little 
while before and after noon, we shall find the shadow 
slowly decrease in length as the sun rises to its culmina- 
tion; and immediately after passing the meridian the 
shadow commences to increase in length. Mark the point 
where the shortest shadow fell, and the line joining this 
point with the foot of the gnomon is a north and south 
line, and on this line all the noon shadows will fall 
throughout the entire year. 

By a careful examination it was discovered that the 
noon shadow on the day of the winter solstice or southern 
limit always fell on the same point. The same was true of 
the noon shadow on the day of the summer solstice or 
northern limit. These points were exactly opposite each 
other on the sun's apparent orbit (or path among the 
stars). It was further discovered, that selecting any day 
in the year, the noon shadow for that day invariably fell 
on the same point as it had done on preceding years ; and 
hence it became manifest that the sun's track among the 
stars did not change from year to year. 

The question now arose as to the figure of the sun's 
path: was that figure a circle? ami did the sun move 
with uniform velooity? As all the stars described diur- 
nal circles ; as this curve was the simplest as well as the 
most beautiful o\' curves ; as its curvature was every where 



20 



THE SUN 



the same ; as it had neither beginning nor ending, it was 
earl j adopted as the celestial curve, shadowing forth, 
even in its form, the ceaseless journeys of the revolving 
worlds. It was assumed then that the sun swept round 
the sphere of the heavens once a year, with uniform 
volocity, in a circular orbit, of which the earth was in the 
center. 

This hypothesis accounted fully for all the discovered 
phenomena, and justly ranks among the most important 
of the primitive discoveries. 

The gnomon gave to the old astronomers a ready 
means not only of tracing the sun's path among the stars, 
but also of measuring the inclination of the plane of the 
ecliptic to the plane of the equinoctial. This is readily 
seen from the subjoined figure. 




Let AB represent the gnomon, A' the shadow of the 
vertex at noon on the day of the summer solstice, and 
A." the shadow at noon on the day of the winter solstice. 
Then will the angle A 'A A" measure the entire motion 
of the sun from north to south ; and as one half of this 
motion lies north and the other half south of the equinoc- 



T H E S U N . 21 

tial, it follows that half the angle, A' A A/' measures the 
inclination of the ecliptic to the equinoctial. 

In the earliest ages it was assumed that the sun's orbit 
was absolutely fixed among the stars, and that the points 
in which this circle crossed the equinoctial were in like 
manner invariable. These points of intersection are of 
the highest importance. That one through which the 
sun passes in going from south to north, is called the 
Vernal Equinox, while the opposite point, through which 
the solar orb passes in going from north to south, is 
called the Autumnal Equinox. On the day of the 
equinoxes, as the sun's center was then on the equinoc- 
tial, the diurnal arc described by the sun would lie one 
half above, and the other half below the horizon, making 
the length of day and night precisely equal. 

Among the ancient nations the day of the vernal equi- 
nox was an object of especial interest, as it heralded the 
coming of spring, and its approach was marked by the 
rising of a certain bright star in the early dawn of the 
morning. Now, in case the vernal and autumnal equi- 
noxes were invariable, the same star by its heliacal 
rising, (as it was called,) would mark the crossing of the 
equinoctial by the sun in the spring and the equality of 
day and night. After the lapse of few centuries it was 
discovered, by the length of the noon shadow of the gno- 
mon, that the sun had reached the equinoctial point, and 
yet the sentinel star did not make its appearance. Either 
the equinox or the star was in motion. It was soon 
decided that the vernal and autumnal equinoxes are both 
slowly moving backwards along the equinoctial and thus 
the sun crosses this celestial circle each year a little be- 
hind the point of the preceding year. 

The ancient nations all seem to have attained to a 



22 THE SCX. 

knowledge of this great truth, and some of them are said 
to have fixed the period in which the vernal equinox 
retrogrades around the entire heavens, a period of nearly 
twenty-six thousand years ; as this is a matter of simple 
observation, and as the rate of motion can be obtained by 
comparing recorded observations, made at intervals of 
four hundred or five hundred years, we may readily cre- 
dit the statement that this period became known even 
anterior to the commencement of authentic history. 

This discovery of the retrocession of the equinoxes led 
to a more critical examination of the sun's apparent mo- 
tion. This motion had been assumed to be uniform, and 
in case this hypothesis could be maintained, the solar orb 
ought to occupy an equal amount of time in passing over 
the two portions of its orbit north and south of the equi- 
noctial, that is, the number of days from the vernal to 
the autumnal equinox ought to be precisely equal to 
the number of days from the autumnal to the vernal 
equinox. 

The Greek astronomer Hipparchus was the first to dis- 
cover the important truth that an inequality existed in 
these two periods. He found from his own observations 
that the sun occupied eight days more in tracing the 
northern than it did in traversing the southern portion 
of its orbit. This was a discovery of the highest import- 
ance, as it seemed to involve the then incredible fact, that 
the lord of the celestial sphere, the great source of life, 
and light, and heat, traveled among the stars with a vari- 
able velocity. 

In case the solar orbit was indeed a circle, this in- 
equality of motion seemed to be impossible. The circular 
figure of the orbit could not be abandoned, neither was it 
possible on philosophical principles to give up the hypo- 



THE SUN. 23 

thesis of uniform motion. Here then was presented a 
problem of the deepest interest, to preserve the circular 
figure of the solar orbit and the uniform motion of the 
sun, and at the same time render a satisfactory account 
of the inequality discovered in the periods during which 
the sun remained north and south of the equinoctial. 
This problem was solved by Hipparchus; and before pro- 
ceeding to examine the reasoning of the old Greek, let 
the student exercise his own genius in an attempt to ex- 
plain the ascertained facts. 

Hitherto it had been assumed, not only that the sun's 
orbit was circular, and that his motion was uniform, but 
also that the earth occupied the exact center of the circle 
in which the sun traveled round the heavens. By pro- 
found study Hipparchus discovered that all the facts 
could be explained by giving to the earth a position not 
in the center of the sun's orbit, but somewhat nearer to 
that portion of the solar orbit where his motion was 
most rapid. This will become evident from the figure. 
Let the circle A BC D represent the sun's circular 
orbit, in which the sun is supposed to move uniformly. 
This motion will only appear uniform to a spectator at 
the center 0. If the observer be removed to 0', and 
the line E E' be drawn perpendicular to 0', the por- 
tion E' A B E of the orbit will require a longer time 
for its description than the portion E C D E , and hence 
in the former the sun will appear to move slower than 
in the latter. Indeed, it is manifest that the point Y. 
on the lino 0' prolonged, is the place of swiftest 
motion, while the opposite point X is that in which 
the sun will appear to move slowest. 



24 



THE SUN 



Hipparchus, not satisfied with thus rendering a general 
explanation of the phenomenon, undertook to determine 
the actual place of the earth inside the solar orbit, or 
the value of the distance 0', which is called the eccen- 
tricity. Here is another problem for the examination of 
the student. It may be solved by simply knowing how 
E F 




E' T 



many days longer tne sun remained north of the equi- 
noctial than it did on the south of this circle. Thi3 
quantity we have already given. By dividing the circle 
ABCD into as many equal parts as there are days in 
the year, and by drawing F F' through the center 0, 
and perpendicular to Y V, we have only to lay off from 
F to E half the excess in days, and draw E E' parallel 
to F F', and it will give at 0' the true place of the earth, 
and 0' will be the eccentricity. An observer at 0' 
will see all phenomena actually detected in the sun's 
motion, while the circular orbit and uniform velocity are 
rigorously retained. 

Having determined the earth's eccentricity, it was now 



THE SUN. 25 

very easy to calculate the sun's place from day to day 
during his entire revolution among the fixed stars. This 
was 1 actually done by the old astronomers ; and as the 
computed places agreed with those observed within the 
limits of observation, with the rude instruments then in 
use, no further advance would be made in the solar mo- 
tions. 

Eclipses of the sun. — No one has ever beheld the 
total disappearance of the sun in the day-time without a 
feeling of awe creeping through his frame, and, even now, 
when modern science predicts the coming of these amazing 
phenomena with unerring precision, a total eclipse of the 
sun never fails to inspire a certain feeling of gloomy ap- 
prehension. What, then, must have been the effect in 
the rude ages of the world of the fading out of the sun in 
mid-course through the heavens? Human genius, of 
course, bent all its energies to the resolution of the great 
problems involved in the occurrence of an eclipse of the 
sun. The first effort was directed to the discovery of the 
cause of these startling phenomena ; and, this once de- 
termined, the second great effort was put forth to so 
master all the circumstances as not only to explain the 
eclipse but to predict its coining. 

Cause of a solak eclipse. — In searching for the 
cause by which the sun might be hidden, it was at once 
evident that there was but one object in the heavens suf- 
ficiently large to hide the whole surface of the sun. This 
body was tho moon. Thus attention was directed to the 
lunar orb, and it was soon noticed that, while the bright 
stars and planets became visible in the darkness attending 
an eclipse of the sun, yet the brightest object in the heavens 
after the sun, was never visible during an eclipse. The 
moon was found to move among the stars with a velocity 



26 THE SUN. 

far greater than that of the sun. It was, moreover, seen 
that the moon's path crossed that of the sun twice during 
every revolution of the moon, and examining still more 
closely, it was discovered that no eclipse of the sun ever 
occurred except at the new moon. Now this rapidly 
revolving globe was evidently the nearest to the earth of 
all the heavenly bodies. It was seen, when a silver 
crescent, sometimes to pass over and hide the larger stars 
which fell in its path ; it was also found that the moon, 
though invisible during a solar eclipse, always appeared 
immediately after very near the sun and as a slendei 
crescent of light. These facts all combined to prove 
beyond a question that the sun was eclipsed by being 
covered by the dark body of the moon. The cause of 
the eclipse was thus reached, and it now remained to rob 
the phenomenon of its terrors by predicting when it might 
be expected. 

To predict a solar eclipse with precision is a problem 
of great difficulty, even with the present extended knowl- 
edge of the laws and structure of the solar system. And 
yet we are informed that the old Greek astronomers suc- 
ceeded in the resolution of this complex problem. This 
may have been done by long and persevering care in the 
record of these phenomena ; for in case all the eclipses 
visible at any given place are recorded year after year 
for a period of nineteen years, it will be found that for 
the next period of nineteen years eclipses will happen on 
the same days and in the same order ; so that an astron- 
omer, whose diligence had been rewarded by the discovery 
of this grand truth, might acquire the highest renown 
among his countrymen and throughout the world by his 
superior wisdom in predicting the coming of an eclipse, 



THE SUN. 27 

though no special genius was put forth in the resolution 
of this great problem. 

We are not quite certain, however, that the prediction 
of the first announced solar eclipse may not have been 
accomplished by the application of powerful thought and 
persevering observation. In case the effort were now 
made to predict a solar eclipse ; as a starting point we 
know that no eclipse of the sun ever occurred except at 
the new moon. But at the time of a total eclipse of the 
sun the moon is interposed precisely between the eye of 
the observer and the sun, and a line joining the centers 
of these two great luminaries, produced to the earth, 
passes through the place of the observer. Hence, on the 
day and at the hour of an eclipse the new moon must be 
in the act of passing from one side of the sun's path to 
the other. To render an eclipse possible two conditions 
must be fulfilled at the same time ; the moon must be 
new, and the moon's center must be in the act of class- 
ing the sun's orbit. If the sun's annual route in the 
heavens were marked among the stars by a line of golden 
light, and the moon's motion be attentively watched, it 
will be found that at every one of her revolutions she 
crosses this golden line twice. The point of her crossing 
from south to north is called the moon's ascending node, 
while the point of crossing from north to south is the 
descending node. 

These nodes do not remain fixed, but are in compara- 
tively rapid motion, and finally accomplish an entire rev- 
olution around the heavens, on the ecliptic. If, then, 
we unite all these facts it will be seen that to produce to 
any observer an eclipse of the sun, the moon, at the new, 
must be exactly in one of her nodes, so that the center 
of the moon, the node, and the center of the sun, form one 



28 THE SUN. 

and the same straight line. Here, then, are the con- 
ditions precedent to a solar eclipse. It now remains to 
so follow these revolving orbs as to be able to anticipate 
the certain occurrence of these determined conditions. 
We follow, then, from night to night, the waning moon ; 
she slowly approaches the sun ; her light becomes a 
delicate crescent, just visible in the gray twilight of 
morning before the rising of the sun ; at length the moon 
becomes invisible, and when she reappears it is on the 
opposite side of the sun, and her silver crescent of light is 
just above the setting sun. There was no eclipse be- 
cause this new moon did not fall on the sun's path. It 
is, however, easy to mark the time of new moon, and 
equally easy to see and note the time when the moon is 
in her node, or on the ecliptic, and by thus watching, 
from new moon to new moon, we may see whether the 
interval from the passage of the node up to new moon is 
growing shorter, and at what rate it decreases, till, 
finally, we shall perceive that on the coming of a cer- 
tain new moon it must fall precisely at the node, and on 
the day of this computed conjunction, to him who has 
watched, and waited, and pondered, and computed, the 
sun must fade away in total eclipse.- Such is the train of 
reasoning and observation which may have first led to the 
resolution of this great problem, but to whose genius we 
are indebted for this grand discovery neither history nor 
tradition furnish any information. 

In consequence of the near equality in the apparent 
diameters of the sun and moon, and a slight change in 
both due to a change of the actual distance from the 
earth (as will be shown hereafter), it sometimes happens 
that the moon's diameter is less than that of the sun. 
When this obtains during a solar eclipse there remains 



THE SUN. 29 

around the black disk of the moon a brilliant ring of 
solar light, and the eclipse is said to be annular. When- 
ever the moon's center, at the new, is not precisely at 
the node, but not so remote from it as the sum of the 
semi-diameters of those two orbs, there will be a partial 
obscuration of the sun. 

We have presented these facts in this place, as known 
to the early astronomers, and as admirable means of exer- 
cising the power of thought on the part of those who may 
desire to devote themselves to the real study of the great 
phenomena of nature. We will recur to this subject 
again when we shall have mastered the laws of motion 
and of gravitation. 

Such is a rapid survey of the discoveries of the an- 
cients in the study of that great orb, which, from its 
splendor, even if it be a mere phantom of light, justly 
commands our admiration and deserves our best efforts 
to master its mysterious movements and its sublime phe- 
nomena. 

We now proceed to exhibit those discoveries which 
could only be accomplished after man had armed himself 
with instruments of great power and delicacy, and with 
a vision increased a thousand fold beyond that, with 
which he is endowed by nature. 

Discoveries of the moderns. — The rude instru- 
ments employed by the early astronomers sufficed to fix 
the places of the sun and the other heavenly bodies with 
sufficient accuracy to give a general outline of the carves 
they described, and as these curves, as determined by 
observation, approximated the circular form, it was con- 
cluded that the deviations from that exact figure were 
only errors of observation. Knowing the period in which 
the sun revolves round the heavens, and the distance of 



30 THE SUN. 

the observer from the center of his assumed circular orbit, 
it was easy to compute accurately the sun's place among 
the stars on any day of the year. This computation 
being made, no instrument then in use could detect any 
difference between the computed place and that actually 
held by the sun. It was, therefore, unphilosophical to 
doubt the absolute truth of an hypothesis thus sustained 
by the best observations which could then be made. It 
was not at all difficult to observe roughly mere position, 
and any error of observation in fixing the place of the 
sun would, in the long run, be eliminated in its effects 
by taking into account a large number of revolutions. 
The degree of accuracy required in thus fixing the sun's 
place among the stars was widely different from that 
demanded in the 

Measukement of the sun's distance. — The prin- 
ciples involved in the solution of this great problem were 
well understood by the old Greek astronomers, and were 
applied by them successfully in measuring the distances 
of inaccessible objects on the surface of the earth. These 
principles are so simple that a knowledge of the very 
first rudiments of geometry will suffice to render intelli- 
gible the methods which are employed in obtaining the 
data for computing the distances of the heavenly bodies. 

Suppose it were required to learn the distance of the 
object A from the point C. From C send to A the visual 
ray C A, then lay off any line from C B perpendicular to 
A C, and measure its length. From B draw the visual 
ray B C, and measure the angle C B A. We have 
thus formed a right-angled triangle, in which the angle 
at C is a right angle,, the base, C B, is known by mea- 
surement, and the angle C B A is known in the same 
way, hence may be computed, by the simplest elements 



THE SUN. 31 

of trigonometry, the length of the distance C A, or the 
required quantity. 

Any error committed in the measurement of the angle 
C B A grows more powerful in its effect on C A, in pro- 



is 



portion to the number of times C B must be taken to 
measure C A. In our attempt to measure the sun's dis- 
tance we are limited to a base line equal in length to the 
eartNs diameter, and hence it becomes necessary to em- 
ploy every refinement of art to eliminate as far as pos- 
sible the errors involved in the measurement of the angle 
C B A, or its complement, the angle C A B, on which, 
in the application of these principles to the problem in 
question, depends the measurement of the sun's distance. 
This quantity is the great key which unlocks all the mys- 
teries of the entire system. Upon it depends directly 
the mass, volume, and density of the sun, the distances, 
weights, and magnitude of all the planets, and even the 
masses and distances of the fixed stars. It is for this 
reason that modern science has spared neither time nor 



32 T H E S U N . 

money, neither skill nor ingenuity in the effort to reach 
an exact solution of this grand problem. 

The solar parallax. — In case an observer were 
located at the sun's center, and from his eye two visual 
rays were drawn, one to the center of the earth, the 
other tangent to the spherical surface of the earth, these 
rays would form an angle with each other at the eye of 
the observer, and this angle is called the sun's horizontal 
parallax. 




Thus S representing the sun's center, C the center of 
earth, C R a radius of the earth perpendicular to the 
visual ray S C, and S R the visual ray drawn to the ex- 
tremity R of the radius, the angle R S C is the solar 
parallax, and in case it were possible to measure that 
angle, as the angle S C R is a right-angle, the remaining 
parts of the triangle R S C become known by computa- 
tation. Thus it appears that the problem of measur- 
ing the sun's distance from the earth resolves itself into 
obtaining the value of the sun's horizontal parallax, 
or the angle under which the earth's radius would be seen 
from the sun's center. 

No instruments have yet been constructed sufficiently 
delicate to accomplish directly the measure of this im- 
portant quantity with the requisite precision. But there 
is an indirect method, which has been employed by 
modern astronomers to accomplish the same object, which 



THE SUN. 33 

has been rewarded with satisfactory success. This method 
we shall now proceed to explain. 

From the most remote antiquity it has been known 
that there are two planets, Mercury and Venus, which 
appear to revolve around the sun, never receding from 
that orb beyond certain narrow and well defined limits. 
The distances from these planets to the sun are less than 
the earth's distance from the same luminary, and hence 
they must at each of their revolutions pass between the 
earth and sun. Modern science has confirmed these an- 
cient discoveries, and the telescope has even shown that 
on certain rare occasions each of these planets actually 
passes between the solar disk and the eye of an observer 
on the earth, and appears as a round black spot on the 
bright surface of the sun. These passages of the planets 
across the solar disk are called transits, and it happens 
that the transits of Venus furnish an admirable means 
of reducing the errors involved in the direct measure- 
ment of the solar parallax, as we shall now proceed to 
explain. 

We will first present the principle involved, and then 
make the application. 

Let it be required to determine the distance of the 
point A from any inaccessible surface, as C D, and that 
A A' is the longest base line which can possibly be em- 
ployed. In case the distance of the point B' on the sur- 
face C D be required, then the angles B' A' A and B A .V 
must be measured, and their sum, subtracted from 180°, 
gives for a remainder the angle ABA', or the angle 
under which the line A A' would be seen In' a spectator 
atB'. Now this angle, because of its minute value, may 
be difficult to measure, ami we desire to find some arti- 
fice by which this difficulty may be at least diminished, 



34 



THE SUN 



if not entirely removed. Suppose then a material point 
to be located at B, much nearer to A A! than to CD, an 
observer at A would see the point B projected on C D at 
B", while an observer at A' would see the same point 




projected at B'. Now let us suppose that the points B' 
and W can be identified and seen as round, black, perma- 
nent spots on the remote surfaee CD; in case B is fur- 
ther from C D than from A A', it is clear that the visual 
angle subtended by B B", as seen from A, will be larger 
than the visual angle subtended by A A', as seen from B', 
in the proportion of the distance B B to the distance BA' ; 
and if B B' should be 2} times longer than B A', then 
would B'B r/ be 2i times longer than A A'; and the prob- 
lem resolves itself into the measurement of the large 
angle B' A B" instead of the small angle A B A'. 

Such is the principle ; and we will now proceed to its 
application. A A' is the diameter of the earth. B is the 
planet Venus, and C D is a diameter of the solar disk. 
To an observer at A, Venus is seen on the sun as a black 
spot at B", while an observer at A! sees the planet pro- 



THE SUN. 



35 



jected at B'. Venus is about 2\ times further from the 
Bun than from the earth, hence B B' is 2 J times longer 
than BA', and therefore B'B" is 1\ times greater than 
AA', or 2| times greater than the diameter of the earth, 
as seen from the sun, or Jive times greater than the sun's 
horizontal parallax ; it is therefore but one fifth part as 
difficult to measure the angle B'AB" as to measure the 
angle A B' A. 

There is another important advantage gained m using 
the transit of Venus in the measurement of the solar 
parallax, arising from the fact that modern science has 
obtained a very exact knowledge of the relative velocity 
of Venus across the solar disk. 




If we note, then, exactly the moment the planet is in 
contact with the solar disk at p, and also at p', this inter- 
val of time will give an enlarged measure of the ehord pp', 
described by the planet as seen from the station A. In 
like manner the observer at A' making the same observa- 



36 THE SUN. 

tions at q and q', we shall obtain the relative lengths of these 
two chords, and hence an accurate measure of the inter- 
val B' B", by which they are separated, or of five times 
the solar parallax. 

Although this problem may appear somewhat complex 
at the first, careful study will render it, in these general 
outlines, very simple and easily intelligible. Its high 
value in the measurement of the very most important ele- 
ment in the entire system of the sun and his satellites 
should secure from the student all the time and attention 
necessary to its complete mastery. 

Such is the importance attaching to this great problem, 
that at the last transit of Venus, governmental expedi- 
tions were fitted out at great expense, and observers were 
dispatched to points on the earth's surface as far asunder 
as possible, each observer noting, with every precaution, 
the exact time in hours, minutes, and seconds, from the 
first contact of the planet with the sun's disk, up to the 
moment of last contact. 

It will be seen that the problem, as presented above, 
is freed from many complications which surround it in 
practice, such as those arising from the revolution of 
the earth in its orbit, its rotation on its axis, and the 
fact that the observers are not located at the extremities 
of the same diameter of the earth. These and other 
matters affecting the result being carefully taken into 
account, we have obtained, for the value of the sun's hori- 
zontal parallax, when at his mean distance from the 
earth, 8 ".6, or eight and six-tenths seconds of arc, 
showing that this grand orb is removed from the earth to 
a distance of about ninety- five millions of miles. 

We shall recur to the transits of Mercury and Yenus 
when we come to treat of those bodies. 



THE SUN'S LIMB 




SOLAR SPOTS 



THE SUN. 37 

The sun's real magnitude.— Modern instruments 
enable us to measure with great exactitude the angle 
subtended by the sun's apparent diameter, an angle whose 
value at the sun's mean distance amounts to 32' .1". 
But a globe removed to a distance of ninety-five mil- 
lions of miles, and yet having an apparent diameter 
of 32'.1", must have a real diameter of no less than 
882,000 miles in length, or more than one hundred and 
eleven times longer than the diameter of our earth, as we 
shall hereafter see. This enables us to compare the bulk 
or volume of these two globes, and we find that it would 
require no less than one million three hundred and eighty- 
four thousand four hundred and seventy-two globes as 
large as the earth to fill the vast interior of a hollow 
globe as large as the sun. This is a comparison of bulk 
only ; the relative weights of the earth and sun must be 
considered hereafter. 

If this wonderful globe excited our admiration by the 
splendor of its surface, and its floods of light and heat, 
how must this admiration be increased when we contem- 
plate its great distance and its gigantic proportions ? 

The physical constitution of the sun. — But for 
the aid derived from the telescope man could never have 
passed beyond mere conjecture as to what lies on the sur- 
face of the sun. The telescope, however, magnifying a 
thousand times, transports the observer over a vast pro- 
portion of the distance separating him from the solar orb, 
and plants him in space within ninety-five thousand miles 
of the sun's surface, there to examine the phenomena re- 
vealed to his sight by this magic tube. We may, there- 
fore, regard the sum's distance as reduced to the thou- 
sandth part oi' its actual value, and we should not be 
surprised to hud upon a globe of such grand proportions 



38 THE SUN. 

fluctuations and changes which, at this reduced distance, 
may become distinctly visible. This anticipation has not 
been disappointed. 

The solar spots. — To the naked eye the sun's sur- 
face presents a blaze of insufferable splendor, and even 
when this intense light is reduced by the use of any 
translucent medium, the entire disk appears evenly 
shaded, with a slight diminution of light around the cir- 
cumference, but without visible spot or variation. When, 
however, the power of vision is increased a hundred or a 
-thousand fold by telescopic aid, and when the intense 
heat of the sun and his equally intense light are reduced 
by the interposition of deeply colored glasses, the eye re- 
cognizes a surface of most wonderful character. Instead 
of finding the sun everywhere equally brilliant, the tele- 
scope shows sometimes on its surface black spots, of very 
irregular figure, jagged and broken in outline, and sur- 
rounded by a penumbra conforming in figure to the gen- 
eral outline of the central black spot (called the nucleus,) 
but of much lighter shade. Even where there are no 
spots, the surface of the sun i3 by no means uniformly 
brilliant. The entire surface has a mottled appearance, 
with delicate pores or points, no one of which can be 
readily held by the eye, but a group of them may some- 
times be seized by the vision under favorable atmospheric 
circumstances, and can be held long enough to demon 
strate that these minute pores do not change their relative 
position, or disappear while under the eye. 

Besides the mottling of the surface, the telescope de- 
tects in the solar orb a variety of brighter streaks, called 
faculce, whose appearance has been connected, as some 
believe, with the breaking out of the black spots. 

Watching from day to day a single spot, or a group 



THE SUN. 39 

of spots ? on the sun's surface, they are found to advance 
together in the same direction, slowly to approach the 
edge of the sun, finally to disappear from the sight, and 
after a certain number of days to re-appear on the op- 
posite side of the sun's disk, revealing the surprising 
fact that the sun is slowly rotating on an axis whose 
position seems to be invariable. In case these spots were 
absolutely fixed on the sun's surface, they would reveal 
the exact period in which his rotation is performed, but 
in consequence of their change of figure, and change of 
position as well, we can only reach an approximate value 
of the period of rotation. This is now fixed, by the best 
authorities, at twenty-Jive days, eight hours and nine 
minutes. 

During the past thirty years M. Schwabe, of Dessau. 
has given special daily attention to counting the groups 
and spots on the sun, and by preserving a record it has 
been discovered that the amount of solar surface covered 
by the black spots is not only variable but that period- 
icity marks this variation. The entire change, from a 
maximum of spots counted in any year, to the mini- 
mum, occupies about five and a half years, and the same 
time elapses from a minimum to a maximum, making 
the period from maximum to maximum eleven years. 
This fact is one of the most surprising revealed in the 
physical constitution of any of the heavenly bodies, and 
thus far has baffled the power of human investigation to 
explain it, while its mysterious character is increased by 
the fact recently discovered, that tins periodicity in ihe 
solar spots is identical in duration with a certain varia- 
tion observed in the intensity of terrestrial magnetism. 
Thus, it would seem, that a new bond of anion is about 
to be established between the earth we inhabit and that 



40 THE SUN. 

mighty orb whence we receive our supplies of light, and 
heat. 

Some astronomers account for the solar spots by sup- 
posing the sun to be a solid, dark, opaque globe, sur- 
rounded by two atmospheres, the exterior one a highly 
luminous and gaseous envelope, the interior more dense, 
and possessing great reflecting power. The spots are 
supposed to result from powerful internal convulsions, 
upheavals from within breaking through these two en- 
velopes, and producing a more extended chasm in the 
external luminous atmosphere. I have examined the sur- 
face of the sun and closely observed the large solar spots 
with a refractor of admirable performance, and so far 
from presenting an appearance such as the above hypoth- 
esis would warrant, the entire exhibition resembled the 
openings often found by melting through a thick stratum 
of solid ice from below — the spiky and jagged outline of 
the black nucleus being well represented by a similar 
form in the opening through the ice, while the penumbra 
was very faithfully represented by the thinner portions 
of ice remaining around the opening. It is not to be in- 
ferred from this comparison that the author entertains 
the opinion that the exterior of the sun is a solid crust, 
and that these solar spots are produced from the melting 
of this crust by the action of internal fires. The com- 
parison is made for the purpose of illustrating, as strongly 
as possible, the absolute appearance of these inexplicable 
phenomena, and to present as strong a contrast as the 
facts warrant to the statement made by a distinguished 
astronomer, that the sun's surface, when viewed by a 
powerful telescope, resembles "the subsidence of some 
floculent chemical precipitates in a transparent fluid. " 
So far from this being the case, the sharp outlines of the 



THE SUN. 41 

penumbra surrounding the dark spots has often been seen 
to cut directly across the minute pores, dividing them 
sharply and sometimes equally. 

Recent observations seem to demonstrate that what has 
generally been considered the solar surface is really the 
exterior of a cloudy atmosphere beneath the luminous 
ocean surrounding the sun. Mr. Dawes, by an eye-piece 
of his own construction, bearing a metallic diaphragm, 
in which a minute hole is pierced, coincident with the 
axis of the telescope, has been enabled to make a very 
critical examination of the solar spots. He finds in the 
center of the dark spot a smaller opening, which is, as 
now seen, intensely black, and this is at present regarded 
as the real surface of the solar orb. The same distin- 
guished observer has announced the discovery of an actual 
rotation of the solar spots about a central axis. This 
important fact has given rise to speculation as to the 
probable cause of these wonderful fluctuations which occur 
in the solar atmospheres. 

It is conjectured that these exhibitions may be pro- 
duced by tremendous storms or whirlwinds resembling 
those which sometimes sweep over the surface of the 
earth, and whose vortices, if seen from above, would 
present an appearance not unlike the spots on the sun. 
We understand how these tornadoes are generated in tho 
atmosphere of the earth, but it is useless to attempt to 
conjecture the causes which can produce such amazing 
effects in the solar atmosphere. 

Intensity of the solab heat. — Admitting that 
the heat of the sun tailing on the earth is diminished in 
the ratio of the Bquare oi' the sun's distance, it is not diffi- 
cult to form some approximate idea of the intensity oi' the 
solar heat at the surface of the sun. By exposing a sur- 



42 THE SUN. 

face of ice to the direct action of the sun's heat, when the 
sun was nearly vertical, Sir John Herschel determined 
by experiment the thickness of the ice melted in a given 
time. 

From this and like experiments it is determined that it 
would require the combustion of more than one hundred 
and thirty thousand pounds of coal per hour on each 
square foot of the sun's surface to produce a heat equal 
to that radiated from the solar orb. 

When an image of the sun is received on any surface 
it is found that the central point of the image is more 
heated than the parts near the circumference, and that 
the temperature diminishes from the equator toward the 
poles. 

The sun's atmosphere. — These facts have been ac- 
counted for by supposing the sun to be surrounded by a 
dense atmosphere, and that the heated rays which pass 
through the deepest part of this atmosphere lose a por- 
tion of their heat, and hence the regions around the disk 
of the sun should be, to us, less heated than those near 
the center of the solar orb. There are some phenomena 
attending a total eclipse of the sun which seem to sustain 
this hypothesis of a solar atmosphere. At the moment 
the eclipse becomes total, there is seen to burst from the 
jet black disk of the moon a sort of halo or glory, radia- 
ting on every side, and presenting a spectacle of won- 
derful grandeur, so much so that on the occasion of the 
eclipse of July, 1842, witnessed at Pavia, the entire 
populace burst into a shout of wonder and admiration. 

There also appeared, at the same time, flames of fire 
darting from behind the limb of the moon, resembling 
mountains of rose-colored light, rising to the height of 
forty or fifty thousand miles above the surface of the sun. 



THE SUN. 43 

These flames are known to assume the form of cloudy 
exhalations which, in some instances, seem to be drifted 
like smoke ascending in a calm atmosphere to a certain 
level, where it meets a current and is borne off horizon- 
tally. 

There is another phenomenon attending the rising and 
setting of the sun at certain seasons of the year in the 
shape of a vast beam of faint, gauzy light, of lenticular 
form, rising from the point of sunset in the evening, and 
stretching upward in the direction of the sun's path some- 
times 70° or 80°. This is called the Zoadical Light, 
and has long been regarded as the evidence of uncon- 
densed nebulosity, or a material atmosphere surrounding 
the equatorial regions of the sun. The central line, or 
axis, of this luminous beam does not appear to be fixed 
in position, and hence a difficulty arises not readily re- 
moved by the hypothesis of a material atmosphere. 

Some have supposed this mysterious luminous zone to 
be a nebulous ring surrounding our moon, while others 
have regarded it as an immense ring of minute asteroids 
or meteors, revolving round the sun, and slowly subsid- 
ing into this grand luminary, and by the conversion of 
their velocity into heat, as they fall in a perpetual shower 
on the sun, or are burned up in the solar atmosphere, 
keeping up a supply equal to the vast radiation shot forth 
from the sun at every moment of time. While we are 
willing to admit that a material globe, falling into the 
solar atmosphere, may generate immense heat, in pro- 
portion to its magnitude and velocity, it seems quite im- 
possible to adopt the hypothesis that the zodiacal light is 
either a material solar atmosphere or a ring of revolving 
meteors, as it extends to such a vast distance from the 
sun, that if revolving with the sun, as does our at mo- 



44 THE SUN. 

sphere with the earth, the particles would be thrown be- 
yond the control of the sun and would be dissipated into 
space. 

We are compelled to acknowledge that up to the pres- 
ent time science has rendered no satisfactory account of 
the origin of the solar light or heat. Whence comes the 
exhaustless supply, scattered so lavishly into space in 
every direction, we know not. Neither is it possible to 
give a satisfactory solution of the solar spots, or of any 
of the strange phenomena attending their rotation or 
translation on the sun's surface. The idea that torna- 
does and tempests rage in the deep, luminous ocean that 
surrounds the sun, like those which sometimes agitate 
the atmosphere of the earth, has no solid foundation. 
We know the exciting causes of the tornadoes on earth, 
but why such storms should exist in the solar photosphere 
it is in vain to conjecture at present. Doubtless the time 
will come when these phenomena will be explained. Per- 
severing and well-directed observation will, in the end, 
triumph ; but these are matters which must be consigned 
to the researches of posterity. 



CHAPTER II. 

MERCURY, THE FIRST PLANET IN THE ORDER OF DIS- 
TANCE FROM THE SUN. 

Its Early Discovery.— Difficult to be distinguished from the Stars. — 
Elongations. — Motion Direct and Eetrograde. — Sometimes Stationary. 
— Nature of the Orbit. — Variation in tiie Elongation Explained. — 
The Nodf8. — Transit of Mercury. — Inclination of Mercury's Orbit. — 
Mean Distance from the Sun. — Conjunctions. — Phases. — Diameter and 
Volume. 

No discovery made by the ancients gives us a higher 
idea of the care and scrutiny with which their astronom- 
ical observations were conducted than the fact that the 
minute planet Mercury, so difficult to be seen, and so un- 
distinguishable from the fixed stars, was discovered in 
the very earliest ages of the world. That the brighter 
planets, such as Venus and Jupiter, whose brilliancy ex- 
ceeds that of any of the fixed stars, should have been 
detected to be wandering bodies, even in the remotest 
antiquity, is by no means surprising. For in watching 
the sun rising and the sun setting, so as to note, in the 
first instance, the stars nearest to the sun, which were 
the last to fade away, and in the second, those stars which 
were the first to become visible, the change of position 
of the planets Venus and Jupiter could not fail to attract 
the attention of the student of the heavens ; but the 
planet Mercury is so small, and so rarely visible, even to 
the keenest eye, that it is said Copernicus himself, during 
his whole life, devoted to the study oi' the heavens, never 
once caught Sight of this almost invisible world. 



46 MERCURY. 

Mercury, in Lis appearance to the naked eye, is not 
distinguishable from the fixed stars. His close proximity 
to the sun, the fact that he is never visible except near 
the horizon, and the intense brilliancy of his disk give to 
him that twinkling appearance which distinguishes the 
fixed stars. Notwithstanding all these difficulties the 
oldest astronomers managed to acquire a very complete 
knowledge of the principal facts connected with the 
movement of this planet. By a careful and continuous 
examination it was found that Mercury never receded 
more than about twenty degrees from the sun's center. 
The amount of recess, or elongation as it is called, was 
soon discovered to be a variable quantity, a fact which 
demonstrated that in case the planet revolved in a circu- 
lar orbit, inclosing the sun, the sun could not occupy the 
center of this circle. By watching the elongations from 
revolution to revolution, it was found that they varied 
from a minimum of 16° 12', to a maximum of 20° 48'. 
Knowing the amount of this variation, and watching 
carefully the progressive change, it became possible to 
reach a tolerably accurate knowledge of the nature 
of the orbit described by the planet in its revolution 
around the sun. It was soon discovered that in some 
portions of his orbit Mercury advanced with the sun in 
his march among the fixed stars, while in other parts 
of his orbit his motion became retrograde, and in the 
change from direct to retrograde, and the reverse, the 
planet apparently ceased to move, and for a short time 
became stationary. 

It will be seen that all these changes are readily ac- 
counted for by supposing the planet to revolve about the 
sun in a circular orbit, the sun being eccentrically placed. 
If we conceive two visual rays, to be drawn from the eye 



MERCURY. 47 

of the observer, and tangent to the orbit of Mercury on 
the right and on the left, the planet, while traversing that 
arc of its orbit intercepted between the points of contact 
and nearest to the eye, will move direct ; in passing 
through the point of contact after direct motion ceases, it 
will move off in the direction of the visual ray, and hence 
will appear stationary for a short time. In the larger 
portion of its orbit (that remote from the eye) its motion 
must be opposite to that of the sun, and hence retro- 
grade. In coming up to the second point of contact the 
planet will move along the visual ray toward the eye of 
the observer, and hence for a short time will appear 
stationary. 

To account for the variation in the elongations of 
Mercury, we must either suppose the point of nearest 
approach of the planet to the sun, called its perihelion, 
to be in motion, or else we must suppose the spectator to 
be himself moving, and thus to behold the planet, its 
perihelion point, and the sun, under varying relations to 
each other. As the early astronomers assumed the im- 
mobility of the earth, they explained the variations in 
the elongations of Mercury by giving to its perihelion 
point a motion of revolution about the sun. 

It is impossible to follow the planet with the naked 
eye in its close approach to the solar orb, as its feeble re- 
flected light is necessarily overpowered by the brilliancy 
of the sun, but by close observation, and by marking the 
positions of the planet at its disappearance and reappear- 
ance, the old astronomers are said to have reached to a 
knowledge of the fact that tins planet sometimes crosses 
the sun's disk, producing what is called a transit of 
Mercury, identical in its phenomena with the transit 
of Venus, already spoken oi' in connection with the de- 



48 MERCURY. 

termination of the solar parallax. In case the plane of 
the orbit of Mercury were exactly coincident with the 
plane of the sun's apparent orbit, it is manifest that every 
revolution of the planet would produce a transit. As 
this, however, is not the case, and as no central transit 
can occur, except when the planet crosses the visual ray 
drawn from the eye of the observer to the sun's center, 
it is manifest that the planet Mercury, during a central 
transit, must actually pass through the ecliptic from one 
side of this plane to the other. This point of passage 
through the plane of the sun's apparent orbit is called 
the node of the planet's orbit. There are, of course, 
two such points. The planet passes its descending node 
in moving from the north to the south side of the ecliptic, 
and its ascending node on its return from the south to 
the north side. 

It is thus seen that in order to produce a transit of 
Mercury there must be a conjunction of the planet, its 
node, and the sun. Whenever this conjunction is abso- 
lute, Mercury will pass across the sun's center. When 
it is only approximate, the planet will transit a small 
portion of the sun's disk, or possibly pass without contact 
at all. 

An attentive examination of the places of the planet, 
before and after a transit, led to a pretty accurate de- 
termination of the angle under which the plane of the 
planet's orbit is inclined to the plane of the ecliptic. This 
angle was approximately determined by the ancients, 
while modern science fixed it at the commencement of 
the present century at 7°.00'.10' / . 

The motion of Mercury in its orbit is more rapid than 
that of any of the planets thus far discovered, traveling, 
as it does, more than one hundred thousand miles an hour, 



MERCURY. 49 

and performing its entire revolution about the sun in about 
eighty-eight of our days. In case this world has the 
same variety of seasons which mark the surface of our own 
earth, these will follow each other in such rapid succession 
that the longest of them will consist of only about three 
of our weeks. It is not difficult to compute the intensity 
of solar light and heat which falls upon the surface of 
the planet Mercury, in case these be subjected to the 
same modifying influences which exist upon the earth. 
But as we remain in ignorance of the circumstances 
which surround this distant planet, it is vain to specu- 
late upon the physical constitution of a world whose close 
proximity to the sun has thus far shut it out from the 
reach of telescopic examination. 

The distance of the planet Mercury from the sun may 
be readily determined, in certain portions of its orbit, in 
case we know first the earth's distance from the same 
orb. For example, conceive a visual ray to be drawn 
from the earth, tangent to the orbit of Mercury (sup- 
posed, for the present, to be circular) ; place the planet 
at the point of contact, and join the center of the planet 
with the center of the sun ; also join the centers of tho 
earth and sun — the triangle thus formed, having the 
earth, Mercury, and the sun as the vertices of its 
three angles is right-angled at Mercury, while the angle 
at the earth is readily measured, and is nothing more, 
indeed, than the elongation, for the time being, of that 
planet. Hence, in the right nngled-triangle, we know 
the angles and the longest side, extending from the earth 
to the sun, and by the simplest principles of trigonom- 
etry, we can compute the remaining parts — namely, 
the distance of Mercury from the sun and from the earth. 
By this, and by other methods more accurate, it is found 



50 MERCURY. 

that Mercury revolves in an orbit around the sun, and 
at a mean distance of about thirty-six millions of utiles. 

As the entire orbit of this planet lies within the limits 
already assigned, it follows that the planet can never be 
seen in a quarter of the heavens opposite to the sun, or 
can never be in opposition. When nearest the earth, and 
on the right line joining the sun and earth, Mercury is 
said to be in inferior conjunction. When 180° distant 
from this place it is on the other side of the sun, with 
respect to the earth, and is then in its superior conjunc- 
tion. 

The telescope has demonstrated that this planet passes 
through changes like those presented by the moon. When 
in superior conjunction the planet will be seen nearly 
round, as in that position nearly the whole of the illu- 
minated surface is turned toward the eye of the observer 
on the earth. As the planet comes round to its inferior 
conjunction the light gradually wanes, until at inferior 
conjunction a slender crescent of great delicacy and beauty 
is revealed to the eye, provided the planet does not lose 
its light entirely in the passage across the sun's disk. 
These phases of Mercury prove, beyond question, the fact 
that the planet does not shine by its own light, but that 
its brilliancy is derived from reflecting the light of the 
solar orb. 

The degree of precision reached in predicting the 
transits of Mercury indicates, with wonderful force, the 
progress of modern astronomy. The first predicted 
transit which was actually observed occurred in 1631, 
when the limits of possible error were fixed by the com- 
puter at four days ; and hence the watch commenced 
two entire days before the predicted time. 

If the transit had taken place in the night time, the 



MERCURY. 51 

opportunity for verification would have been lost. For- 
tunately this was not the case, and the toil and zeal of 
Gassendi were rewarded with the first view of Mercury 
projected on the solar disk ever witnessed by mortal man. 
Nearly two hundred years later, at the beginning of the 
nineteenth century, the French astronomers ventured to 
assert that their predictions could not be in error more 
than forty minutes. The transit which occurred on the 
8th Nov., 1802, verified this assertion very nearly. By 
a more careful study of the causes affecting the place of 
the planet, forty- three years later, the discrepancy between 
computation and observation was reduced to only sixteen 
seconds of time, a quantity very minute, when we take 
into account the variety of causes affecting the resolu- 
tion of the problem. The transits of Mercury recur at 
certain regular intervals, repeating themselves after a 
cycle of 217 years, falling for the present in the months 
of May and November. 

Having learned the distance of Mercury from the earth, 
and having measured the angle subtended by its diameter, 
we find its actual magnitude to be much smaller than 
that of the earth. Its diameter is but 3,140 miles, and 
its volume is but 0.063, the earth's volume being counted 
as unity. 

In comparison with the vast proportions of the sun, 
this little planet sinks into absolute insignificance, for if 
the sun be divided into a million equal parts Mercury 
would not weigh as much as the half of one of these 
parts. 



CHAPTER III. 

VENUS, THE SECOND PLANET IN THE ORDER OF DIS- 
TANCE FROM THE SUN. 

The First Planet Discovered. — Mode of its Discovery. — Her Elongations. 
— Morning and Evening Star. — A Satellite of the Sun. — Her Superior 
and Inferior Conjunctions.— Her Stations.— Direct and Eetrogradh 
Motions. — These Phenomena indicate a Motion of the Earth. — Transits 
of Venus. — Inclination of the Orbit of Venus to the Ecliptic. — Her 
Nodes. — Intehvals of her Transits. — Knowledge of the Ancients. — 
Phases of Venus.— Her Elongations Unequal.— No Satellite yet Dis- 
covered.— Sun's Light and Heat at Venus. — Her Atmosphere. 

This planet is the second in order of distance from 
the sun. and as it is the most brilliant of all the orbs, 
with the exception of the sun and moon, it was undoubt- 
edly the first discovered of all the planets. The move- 
ments of the sun and moon among the fixed stars must 
have claimed the attention of the observers of celestial 
phenomena in the earliest ages of the world. In marking 
the rising and setting sun, and in noting the stars which 
were the last to fade out in the morning twilight and 
the first to appear in the evening after the setting of the 
sun, the brilliancy of Venus could not fail to have at- 
tracted the attention of the very first observer of celestial 
phenomena. A star of unusual brightness was noticed 
in comparative proximity to the sun in the early evening. 
The sun's place, with reference to this object, having 
been carefully marked, for a few consecutive nights, it 
was found that the distance between them was rapidly 
diminishing. It was readily seen that this diminution of 



VENUS. 53 

distance was due to the fact that the bright star was ap- 
proaching the sun, for by comparing its place among the 
fixed stars with what it was a few nights previous, this 
star was found to have changed its position among the 
group in which it happened to be located, and was evi- 
dently advancing rapidly toward the sun. 

"We are thus presented with the exact facts which must 
have marked the discovery of the first planet or wander- 
ing star ever revealed to the eye of man. We know not 
the name of the discoverer, nor the age or nation to 
which he belonged, but we are satisfied that the facts as 
above stated did undoubtedly occur ; and we find not only 
profane authors but one of the Hebrew prophets referring 
to this planet more than two thousand five hundred years 
ago. The student who desires may easily re-discover the 
planet Venus. She will be readily recognized as the 
largest and brightest of all the stars, and will be found 
never to recede from the sun more than about 47°. From 
this distance, which she reaches at her greatest elonga- 
tion, the planet will be found, at first slowly, but after- 
ward more rapidly, to approach the solar orb. She ay ill 
finally be lost in the superior effulgence of the sun ; and 
when the unaided eye ceases to follow her in her approach 
to the sun, telescopic power will enable the observer to 
continue his observations until, finally, the sun's direct 
beams, mingling with those of the planet, she ceases to 
bo visible, and is now lost for a greater or less period, 
until she emerges from the solar rays, appearing just bo- 
fore the sun in the gray morning twilight. She now 
recedes from her central orb, finally reaches her greatest 
elongation upon the opposite side, stops in her career, 
returns again, and thus oscillates backward and forward, 
never passing certain prescribed limits. 



51 VENUS. 

As already stated, the fact that Venus was a planet or 
wandering star must have become known among the very 
first of astronomical discoveries ; but it required, doubt- 
less, a long series of observations to determine the truth 
that the bright star, which for some months had accom- 
panied the setting sun, and which was at length lost in 
the solar beams, was the same object which, at a later 
period, became visible in the morning dawn, having passed 
by or across the solar disk. This discovery, however, is 
said to have been made by the Egyptian priests, and was 
by them communicated to the Greek astronomer, Pytha- 
goras, who taught this truth to his countrymen. 

It is obvious, from the above facts, that the planet 
Venus, like Mercury, is beyond doubt a true satellite of 
the sun, even to the inhabitants of the earth, and it is 
equally manifest that, whatever be the true relations be- 
tween the earth and the sun, and whichever one of these 
two bodies may be at rest, one thing is certain, the planets 
Mercury and Venus cannot by any possibility have the 
earth for their center of motion. No matter in what 
region of the heavens the sun may be found at any season 
of the year, these two interior planets ever accompany 
him. As Venus recedes to a greater distance from the 
sun than Mercury, it follows that her orbit of revolution 
around the sun must be the larger of the two. We are 
thus enabled, by the simplest train of reason and obser- 
vation, to fix the following facts : — The sun is a central 
orb, about which revolve, in regular order, two planets, 
the nearest of which is Mercury, and next to Mercury, 
Venus, with periods of revolution, readily determined by 
the spectator on the earth's surface. These facts are ex- 
ceedingly important as the primary ones which lead to 
the discovery of the true system of the universe. 



VENUS. 55 

When Venus passes between the eye of the observer 
and the sun, she is said to be in her inferior conjunc- 
tion; when she is directly beyond the sun, with reference 
to the spectator, she is in her superior conjunction. 
From her inferior to her superior conjunction she occu- 
pies a position west of the sun, rises in the early morning, 
before the sun, and is known as Phosphorous, or Lucifer, 
or the morning star. From her superior to her inferior 
conjunction she follows the setting sun ; she becomes 
our evening star, under the name of Hesperus. 

In examining the phenomena involved in the motions 
of Venus, and watching her carefully in her approach to 
and in her recess from the sun, it is found that her move- 
ments are almost identical with those of Mercury — her 
motions for a certain portion of her revolution being 
direct, or like those of the sun ; she then becomes sta- 
tionary, then moves backward or retrograde among the 
fixed stars, becomes stationary again, and then com- 
mences her direct movement. All these facts are readily 
accounted for by admitting that Venus revolves about 
the sun in an orbit nearly circular, and that she is viewed 
by a spectator situated exterior to her orbit, and moving 
around the sun and Venus in a circle, whose plane makes 
a small angle with the plane on which the orbit of Venus 
lies. If a visual ray be drawn from the eye of the observ- 
er, tangent to the orbit of Venus, should the planet hap- 
pen to fill the point of contact, she will appear to move 
in the direction of this ray, and, for the time being, will 
be directly advancing to, or receding from, the eye of the 
observer, and thus will appear stationary. That the ob- 
server is in motion, is manifest from the fact that the 
direct movement of Venus does not bear that relation to 
the retrograde movement which is required by such an 



56 VENUS. 

hypothesis. Indeed, if two visual rays were drawn from 
the eye of a stationary observer, tangent to the orbit of 
Venus, she would appear to move from one point of con- 
tact to the other, on the hither side of her orbit, with a 
direct motion, while on the further side of her orbit, be- 
tween the points of contact, her motion would appear 
retrograde. These facts, however, are not presented in 
nature, and would be subverted, of course, by supposing 
the spectator to be in motion. In case the spectator were 
to occupy the line passing from the sun's centre through 
Yenus, and to revolve about the sun in the same period 
occupied by the planet, then would the planet always be 
seen in inferior conjunction with the sun. As this is not 
the fact in observation, it is manifest that the angular 
velocity of the spectator is not so great as that of the 
planet Yenus, as she finally emerges from the sun's rays, 
after her inferior conjunction, beyond the line, joining 
the sun's center and the eye of the beholder. Here, then, 
is another important fact, which must be taken into ac- 
count when we shall inquire into the true system of na- 
ture, as presented in the organization of the planetary 
worlds. 

In case the eye of the observer were located in the 
same plane in which the orbit of Yenus lies, this plane, 
passing, as it does, through the sun's center, it is clear 
that at every inferior conjunction of the planet there 
might be seen a transit of Venus, while at every su- 
perior conjunction, the planet would be occulted, or hid- 
den, by passing actually behind the disk of the sun. It 
happens, however, that the plane of the orbit of Yenus 
does not coincide with the plane of the ecliptic, or earth's 
orbit. These planes are inclined to each other, under an 
angle of 3° 23' 28". 5, one ,half of the orbit of Yenus 



VENUS. 57 

lying above, or north of the ecliptic, the other half lying 
below, or south of the ecliptic. The point in which 
Venus passes from the north to the south side of the 
ecliptic is called the descending node. She returns from 
the south to the north of this plane through the ascend- 
ing node, and the line joining these two points is called 
the line of nodes. 

The transits of Venus, unfortunately for astronomical 
science, are of very rare occurrence, and are separated 
by intervals of time which are very unequal. The peri- 
ods from transit to transit are 8,122, 8,105, 8,122, &c, 
years, for a long period falling in the months of June and 
December. As already stated, no transit can occur ex- 
cept when the planet is in the act of passing her node at 
her inferior conjunction, while, at the same time, the 
earth is crossing the line of nodes of the planet prolonged. 
This line of nodes, though not fixed, moves very slowly, 
and at this time crosses the earth's orbit in those re- 
gions passed over by the earth in the months of June 
and December. After a transit the relative motion of 
Venus, the earth, and the node of the orbit of Venus, is 
such as to render it certain that within eight years an- 
other transit will occur, as within this period Venus does 
not, at her inferior conjunction, recede too far from tho 
plane of the ecliptic to render her transit impossible. 

In our account of the determination of the solar paral- 
lax (Chap. I) we have stated that the distance of Venus 
is readily determined by the measure of her horizontal 
parallax. Her distance may also be determined, after we 
have learned the distance of the sun, by tho same method 
used in measuring the distance of Mercury (Chap. U). 

By theso and other methods the moan distance of this 
planet from the sun is found to be about sixty-eight 



58 VENUS. 

millions of miles, and from the measure of her apparent 
diameter we conclude her actual diameter to be 7,700 
miles, or a little less than the diameter of the earth, as 
we shall see hereafter. 

The period of rotation of Yenus has not been well de- 
termined, but from an examination of indistinct spots, 
sometimes visible on her face, it is conjectured that she 
rotates on her axis in about twenty-four hours, or in the 
same period occupied by the earth. 

The changes in the brilliancy of the planet Yenus 
are accounted for in a two -fold way. In case the 
observer is really exterior to her orbit, as the planet's 
distance from the sun is on the average 68,000,000 
of miles, then when the planet occupies that point in 
her orbit nearest the observer she will be closer to the 
eye than when in the opposite point of her orbit by an 
amount equal to no less than double her mean dis- 
tance from the sun, or 136,000,000 of miles. We readily 
perceive that this vast increase of distance must diminish 
in direct proportion the apparent diameter of the planet, 
and thus her brightness must decline, as she recedes from 
her nearest to her greatest distance from the observer. 
To this cause, however, of a change of brilliancy, is to be 
added another of still greater importance. We have 
already stated that the planet Yenus, when seen pro- 
jected upon the sun's disk during her transit, ap- 
pears as a round, black spot on the brilliant surfaco 
of the sun. This fact demonstrates, beyond a doubt, 
that the planet Yenus is a dark, opaque globe, destitute 
of light, and only visible by reflecting the light which it 
receives from the sun. If further evidence of this state- 
ment were wanting, it is found in the fact that after the 
planet passes her inferior conjunction and becomes visi- 




PHASES OF VENUS 




VENUS. 59 

ble in emerging from the sun's beams, she is first seen 
by the telescope as a slender and delicate crescent of 
silver light. As she recedes from the sun this phase 
gradually changes; more and more of her illuminated 
hemisphere becomes visible, until, finally, at her superior 
conjunction, her disk becomes round and well-defined. 
The same facts are true of the planet Mercury, and thus 
is added another powerful evidence that these two planets 
are satellites of the sun, revolving about this luminary in 
orbits nearly circular, and deriving their light from this 
great central body. 

When we come to measure accurately the greatest 
elongations of Venus we find them unequal. In case 
the spectator were stationary, and admitting the circular 
form of the orbit of Venus, these inequalities could not 
occur. We thus are led to believe, either that the orbit 
of the planet is not circular, or, if it be circular, that the 
sun is eccentrically situated, or that the observer himself 
is in motion. 

It is possible that any two, or even all of these causes, 
may combine to produce the phenomena presented in the 
movements of Venus. We shall recur again to these 
matters when we come to consider the great problem of 
the true system of the universe. 

The extreme brightness of this planet makes it a very 
beautiful but difficult object for telescopic observation. 
Although spots havo been seen upon the surface of 
Venus, and by their close examination her period of ro- 
tation upon her axis has been approximately determined, 
I have never been able, at any time, with the powerful 
refractor of the Cincinnati Observatory, io mark any 
well-defined differences in the illumination of her sur- 
face. If we are to trust to the observations of others, 



60 VENUS. 

the inequalities which diversify the planet Venus far ex- 
ceed in grandeur those found upon our earth. It is 
stated by Mr. Schroter that, from his own observations, 
the mountains of Venus reach an altitude five or six 
times greater than the loftiest mountains of our own 
globe. 

It has been affirmed by several distinguished as- 
tronomers that this planet is accompanied by a minute 
satellite, but by the application of the most powerful 
telescopes, during the present century, and after the 
most rigid examination, this statement has not been con- 
firmed. It was supposed that during the transit which 
occurred in 1769 the disputed question as to the ex- 
istence of a moon of Venus would be positively settled. 
While the planet was distinctly seen as a dark spot 
upon the surface of the sun, no telescopic power could 
detect any dark object which might be a satellite. Al- 
though we cannot absolutely affirm that Venus has no 
satellite, we may safely say, that if there be one it yet 
remains to be discovered. 

The amount of light and heat which the earth would 
receive from the sun, if revolving in the orbit of Venus, 
would be nearly twice as great as that now received ; but 
this does not justify us in concluding that the planet 
Venus has a mean temperature nearly double that of the 
earth. We know that a powerful influence is exerted by 
the earth's atmosphere to modify the solar heat. There 
may exist an atmosphere surrounding Venus such that 
the temperature at her surface may be no greater than 
our own. It is useless, however, as we have already re- 
marked, for us to speculate about matters concerning 
which we positively know nothing. There are some in- 
dications in the telescopic appearance of Venus that she 



VENUS. 61 

is surrounded by an extended atmosphere. When pre- 
senting the form of a crescent of light, the slender horns 
are found sometimes to extend beyond the limits of a 
semi-circumference — a fact only to be accounted for, so 
far as we know, by admitting atmospheric refraction. 



CHAPTER IV. 



THE EARTH AND ITS SATELLITE : THE THIRD PLANET 
IN THE ORDER OF DISTANCE FROM THE SUN. 

Thh Eabth the apparent Center of Motion. — To all the Senses it is at 
Eest. — The Center op the Motions of the Sun and Moon. — Explanation 
of the Acceleration of the Orbitual Motion of the Sun and Moon. — 
Ptolemy's Epicycles. — The Explanation of Copernicus.— The Sun the 
Center of Planetary Motion. — The Earth One of the Planets.— Ob- 
jections to this Hypothesis. — The Answer. — Sy'stem of Jupiter discov- 
ered by the Telescope. — The Old System superseded by the New. — The 
Figure and Magnitude of the Earth.— How determined.— The Earth's 
Motions. — Eotation and Revolution. — A Unit of Time furnished by 
the Earth's Period of Eotation. — Earth's Orbitual Motion. — Vernal 
Equinox. — Perihelion of Earth's Orbit. — Its Period of Revolution. — 
Solar and Sidereal Time. 

THE MOON.— Revolution in her Orbit.— Her Phases.— Earth's Line. — Ec- 

CENTRIjMTY OF HER ORBIT. — Ee VOLUTION OF HER APOGEE. — INCLINATION OF 

her Orbit. — Moon's Parallax and Distance. — Her Physical Cosstitu 
tion. — Center of Gravity and Center of Figure. 

The ancients did not reckon the earth as one of the 
planetary orbs. There seemed to be no analogy between 
the world which we inhabit, with its dark, opaque, and 
diversified surface, and those brilliant planets which pur- 
sued their mysterious journey among the stars. Sunk 
as they were, so deep in space, it was very difficult to 
reach any correct knowledge of their absolute magnitude. 
The earth seemed, to the senses of man, vastly larger 
than any or all of these revolving worlds. About the 
earth, as a fixed center, the whole concave of the heavens, 
with all its starry constellations, appeared to revolve, 
producing the alternations of day and night. It was not 
unnatural, therefore, knowing the central position of the 



THE EARTH. 63 

earth with reference to the fixed stars, to assume its cen- 
tral position with reference to the sun, and moon, and 
planetary worlds. 

There is no problem perhaps so difficult as that pre- 
sented in the attempt to discriminate between real and 
apparent motion. To all the senses the earth appeared 
to be absolutely at rest. It could not be affirmed that 
any one had ever seen it move, or felt it move, or heard 
it move, while the sense of sight bore the most positive 
testimony to the motion of the surrounding orbs. It must 
be remembered that, in the primitive ages, the great 
objects of observation and study were the sun and moon. 
Five planets were indeed discovered, at a period so re- 
mote that no historic record of the facts of their discovery 
now exists. They seem to have been known to all the 
nations of antiquity, and a knowledge of their existence 
appears to have been derived from a common origin, as 
we shall have occasion to notice more particularly here- 
after. A few of the more obvious phenomena r presentcd 
in the planetary movements were known and studied by 
the old astronomers, but when these motions became to 
them inexplicable, they frankly confessed that these 
matters must be left for the study and development of 
posterity. 

If, then, we confine our attention principally to an 
examination of the solar and lunar motions, and to the 
general revolution of the sphere of the fixed stars, in our 
efforts to determine the true position and condition of the 
earth, we shall find ourselves compelled, as were the 
celebrated Greek astronomers, Hipparchus and Ptolemy, 
to admit not only the earth's central position, but also its 
absolute immobility. It is, undoubtedly, central to the 
moon's motions, and it is equally central to the sun's. 



64 THE EARTH. 

movement ; that is to say, all the phenomena of the solar 
motions are as well accounted for by supposing the earth 
to be the center about which the sun revolves, as by sup- 
posing the converse hypothesis, that the sun is the center 
about which the earth revolves. 

So far, then, as these two great luminaries are con- 
cerned, the hypothesis of the earth's central position is 
well sustained, and almost indisputable. It is only when 
we extend our investigations to the inferior and superior 
planets, and gather together a multitude of facts and 
phenomena demanding explanation, that we find ourselves 
necessarily driven into so great complexity by retaining 
the central position of the earth, that at last we begin to 
doubt. We have already noticed the remarkable move- 
ments of the two planets Venus and Mercury. We shall 
find hereafter that phenomena of a like character were 
presented in the movements of Mars, Jupiter, and Sa- 
turn, each of which planets was distinguished by its sta- 
tions, retrogradations, and advances among the fixed 
stars. The ancients not only adopted the hypothesis of 
the earth's central position and immobility, but, for evi- 
dent reasons, likewise adopted the hypothesis that all mo- 
tion was performed in circular orbits, and with uniform 
velocity. We have already seen, in our examination of 
the solar motions, that this orb did not move to the eye 
with uniform velocity, but this apparent deviation from 
uniformity was readily accounted for by supposing the 
earth to be placed a little eccentric with reference to the 
sun's circular orbit. The same facts becoming known 
with reference to the moon's motion, a like hypothesis 
was adopted, and the earth was placed eccentrically within 
the lunar orbit. In marking the planetary movements, 
they were found, however, to differ radically in some 



THE EARTH. 65 

particulars from the movements of the sun and moon. 
While these great luminaries always advanced in their 
revolution among the fixed stars, the planets were found, 
in making their revolution, not only to stop, but for a 
time actually to turn back, then stop again, and finally 
to resume their onward movement. No eccentric posi- 
tion of the earth could account for these stations and retro- 
gradations ; but a very simple expedient was devised, 
which rendered a satisfactory account, in the primitive 
astronomical ages, of these curious phenomena. Retain- 
ing the central position of the earth and the circular 
figure of the planetary orbits, each planet was supposed 
to revolve on the circumference of a small circle, whose 
center was carried uniformly around on the circumfer- 
ence of the great circle constituting the orbit of the 
planet. By such machinery it will be seen that it be- 
came possible to render a satisfactory account of the sta- 
tions and retrogradations of the planets, for while the 
planet was describing that portion of the small circle in 
which it revolved, nearest to the eye of the spectator, it 
would seem to move backward in the order of the fixed 
stars. Again, in coming directly toward the eye of the 
spectator, or in moving in the opposite direction along 
two visual rays, drawn tangent to its small circle, the 
planet would appear stationary. Such was the general 
exposition of the Greek astronomer Hipparchus, whoso 
theory was enlarged and extended by his successor 
Ptolemy, whose theory of astronomy, based upon the 
central position of the earth, known as the Ptolemaic 
System, endured for more than fifteen hundred years. 
It was only after a long lapse of time, and by the dis- 
covery of a large number of irregularities in the solar, 
lunar, and planetary motions, making it necessary {tu 



6Q THE EARTH. 

render a just account of them) to increase the number of 
these small circles, which were called epicycles, that 
the whole scheme finally became so cumbrous and com- 
plicated that, after long and laborious study, extending 
through more than thirty years of diligent observation, 
the great Polish astronomer, Copernicus, found himself 
compelled to abandon the old hypothesis of the central 
position of the earth, and to attempt a new solution of the 
great problem of the universe. 

In giving up the earth as the centre about which the 
worlds were revolving, there was little difficulty in se- 
lecting the object which, in greatest probability, occupied 
the true center. All the movements of the sun could, 
without the slightest difficulty, be transferred to the 
earth, and thus the sun could become central to the 
earth, revolving as one among the planets. This hypo- 
thesis did not require any change whatever in the com- 
putation of those tables which gave from day to day the 
sun's apparent place among the fixed stars. Again, as 
we have already seen, the planets Mercury and Venus 
were undoubtedly satellites of the sun, whether the sun 
be at rest or in motion ; and with these suggestions, the 
vigorous mind of Copernicus, transferring himself, in 
imagination, to the sun, and thence looking out upon the 
planetary revolutions, found that a large number of those 
complexities and irregularities which had so confounded 
him when viewed from the earth's surface were swept 
away for ever. When seen from the sun, as the center 
of motion, all the stations and retrogradations in the 
planetary revolutions disappeared. The complications in 
the movements of Mercury and Venus were reduced to 
perfect order and simplicity when seen from the sun. 
The earth itself assumed its proper rank among the 



THE EARTH. 67 

planetary worlds, dignified by the attendance of its satel- 
lite the moon, and beyond the earth, the planets Mars, 
Jupiter, and Saturn, performed their orderly revolution 
in orbits nearly circular. Such is the true scheme of 
nature in its grand outlines, as given to the world by 
Copernicus. It will be seen that one of the remarkable 
features of the old system, namely, the uniform circular 
movement of the planets, was retained by the Polish as- 
tronomer. By the use of eccentrics and epicycles, Co- 
pernicus found it possible to render a satisfactory account 
of all the phenomena of the solar system known during 
his age. We can readily comprehend that a system in- 
volving the startling doctrine of the swift rotation of the 
earth upon its axis, and the rapid flight of its entire 
mass, with all its continents, and oceans, and mountains, 
through space, must have been received by the human 
mind with the greatest distrust. Indeed, there seemed 
to be to the eye positive proof that this bold theory was 
absolutely false. It was urged by the anti-Copernicans, 
that in case the earth did revolve about the sun in an 
orbit of nearly two hundred millions of miles in diame- 
ter, that the point where the axis of rotation, prolonged 
to the sphere of the fixed stars, pierced the heavens, must 
by necessity travel around and describe a curve among 
the stars identical with that described by the earth in re- 
volving about the sun. Now, as no such motion of the 
north polar point was visible to the eye, but as the axis 
of the heavens remained for ever fixed among the stars, 
it proved beyond dispute the absolute impossibility of the 
earth's revolution about the sun. This train of reason- 
ing was undeniably true, and the only response which 
the Copernioans could make was this : " The earth does 
revolve about the sun ; the earth's axis prolonged does 



G8 THE EARTH. 

pierce the celestial concave in successive points, describ- 
ing a curve precisely like the earth's orbit, and whose diam- 
eter is indeed nearly 200,000,000 of miles ; but that the 
distance of the fixed stars is so great, that an object hav- 
ing this immense diameter actually shrinks into an in- 
visible point, on account of the almost infinite distance to 
which it is removed from the eye of the beholder;" and 
with this answer the world was compelled to rest satisfied 
for more than two hundred years. 

The doctrines of Copernicus gained a great accession 
of strength by the invention of the telescope. By the 
use of this extraordinary instrument not only were the 
phases of Mercury and Venus detected, but also the 
greater discovery of the satellites of Jupiter, presenting, 
in this central orb, with his four revolving moons, a sort 
of miniature likeness of the grander system, having the 
sun for its center. The simplicity of the hypothesis pre- 
sented in the Copernican system, the numerous compli- 
cations which it removed from the heavens, and the satis- 
factory account which it yielded of the discoveries made 
by the telescope, caused it to be adopted and defended 
by some of the best minds of the age immediately follow- 
ing that of Copernicus, among whom none is more dis- 
tinguished than the great Florentine astronomer and 
philosopher Galileo Galillei. It is hardly necessary to 
mention the historical fact, that the old system of astron- 
omy, which had held its sway over the human mind for 
more than 2,000 years, did not fall without a severe 
struggle. The astronomy of Ptolemy, and the philosophy 
of Aristotle, had taken so deep a hold of mankind, and 
were so firmly interwoven with all the systems of educa- 
tion and of science, that we must behold with astonish- 
ment the downfall of systems venerable from their an- 



THE EARTH, 69 

tiquity, and whose ruin could only be accomplished by 
the desertion of their adherents. 

The figure and magnitude of the earth. — A 
knowledge of the globular figure of the earth seems to 
have been reached at an early period in the history of 
astronomy. Indeed, the concave heavens, presenting to 
the eye a hemisphere above the horizon, and, undoubtedly, 
extending beneath the earth, so as to complete the grand 
hollow sphere, suggested at once that the inclosed earth, 
minute in its dimensions when compared with the celes- 
tial globe by which it was encompassed, might also have 
the globular form. The curvature of the earth's surface 
becomes at once visible to the eye in marking the gradual 
approach of a ship at sea. At first only the top of the 
mast can be discovered, even with a glass, all the remain- 
ing parts of the vessel being hidden by the outline of the 
the interposed water. As the distance diminishes, more 
and more of the ship lifts itself above the horizon, until, 
finally, the water-line comes into sight. The same evi- 
dence of the rotundity of the earth is furnished by the 
circular form of the horizon which always sweeps round 
a beholder who ascends to the summit of a lofty moun- 
tain. Thus, we are disposed to adopt the spherical form 
of the earth in consequence of its simplicity, even before 
we have any conclusive demonstration as to its real form. 

The Greek astronomers comprehended the simple pro- 
cess, whereby not only the true figure of the earth might 
bo obtained, but in case it were spherical, whereby its 
real diameter and absolute magnitude might be deter- 
mined. 

This process is remarkably simple. Suppose an ob- 
server, provided with the means of directing a telescope 
precisely to the zenith of any given station, and in the 



70 



THE EARTH. 



zenith point he marks a star, which from its magnitude 
and position he can readily find again. Now, leaving 
this first station, and moving due north, measuring the 
distance over which he passes, he will find that, as he 
progresses toward the north, the star under examination 
will leave the zenith and slowly decline toward the south. 
Suppose the observer to halt, set up his instrument, and 
find that his star has declined one degree from the zenith 
toward the south. 

This demonstrates that he has traveled from the first 
station to the second, over one degree of a great circle of 
the earth, or one part in 360 of the entire circumference 
of the earth. It follows that, in case the earth is really 
globular in form, the distance between the stations, multi- 
plied by 360, will give the length of the entire circum- 
ference, and this quantity, divided by 3.14159 (the ratio 
between the circumference of a circle and its diameter), 
will give the value of the earth's diameter. 

It is by methods analogous to the above that the true 
figure and actual magnitude of the earth have been de- 
termined. Very numerous and delicate measures, per- 
formed in many parts of the earth's surface, have revealed 
the surprising fact that the true figure of the earth 
is not that of a sphere, but of a spheroid, being more 
flattened at the poles and more protuberant at the equa- 
tor than a true sphere. We shall hereafter exhibit the 
cause of this remarkable fact, and present some very 
curious and surprising results and phenomena which 
flow from it. By the most reliable measure we find the 
polar diameter of the earth to be 7,898 miles, while the 
diameter of the equator reaches to 7,924, being an excess 
of no less than twenty-six miles, which excess would have 
to be trimmed off to reduce the earth to a globular form. 



THE EARTH. 71 

The earth's motion. — We have already noticed the 
fact that the sun, as well as the planets thus far described, 
have a motion of rotation about *a fixed axis, while the 
planets have also a motion of revolution in their orbits. 
Since we are compelled to recognize the earth as one of 
the planets, we naturally conclude that it will be dis- 
tinguished by the same motions which mark the on- 
goings of the other planets. We shall find, indeed, that 
the earth has three motions : a motion of rotation about 
an axis, accomplished in a period of twenty- four hours, 
and producing an apparent revolution of the sphere of 
the fixed stars in the same period. A motion of revolu- 
tion in an orbit whereby the earth is carried entirely 
around the sun, effecting all those changes which mark 
upon the earth's surface the seasons of the year, and pro- 
ducing at the same time an apparent revolution of the 
sun in a circular orbit among the fixed stars. The earth 
has a third motion, (which we will examine more fully 
hereafter,) occasioned by the fact that its axis of rotation 
does not remain constantly parallel to itself. 

The earth's rotation. — Let us return to the con- 
sideration of the diurnal revolution, to the inhabitants 
of the earth, as well as to the student of astronomy, 
by far the most important motion which has been re- 
vealed by human investigation. It is, perhaps, impos- 
sible for the mind of man to form any just notion of 
what we call time, except as its flow is measured by 
some absolutely uniform succession of events. This per- 
fect measure of time is found in the uniform rotation 
of the earth upon its axis, whereby all the fixed stars 
appear to the eye to perform revolutions in circles of 
greater or less diameter, all in the same identical period, 
and with a motion which, so far as we know, is ftbso- 



72 THE EARTH. 

lutely uniform. Thus the duration of one rotation of the 
earth upon its axis, whereby any given fixed star re- 
volves from the meridian of any place entirely round to 
the same meridian again, furnishes to man a unit of 
time, which, by its sub-divisions and multiplications, 
renders it possible to take account of historic and other 
events, and to mark their relations to each other, not 
only in the order of time, but also in the interval of time. 
Thus, a day is sub-divided into hours, minutes and 
seconds, and the fraction of a second, and by successive 
additions gives us larger portions of time, as weeks, 
months, years, and centuries. To serve this very im- 
portant purpose, and to become a true unit of measure of 
time, it is absolutely indispensable that the motion of ro- 
tation of the earth upon its axis shall be rigorously uni- 
form and invariable. 

We have, at present, in all the active observatories in 
the world, a constantly accumulating power of evidence 
that the earth now revolves with uniform velocity. Not 
a star passes the meridian wire of a fixed telescope, true 
to the predicted moment of transit, without testifying to 
the absolute uniformity of the earth's rotation. So far, 
then, as it be possible, by human observation and human 
means, to determine any truth whatever, we are able to 
affirm the absolute uniformity of the rotation of the 
earth upon its axis. This truth is affirmed as of to- 
day ; and so far as we can go back in the history of 
accurate astronomical observation, the same truth is 
affirmed of the past ; and La Place informs us that, from 
a rigorous investigation of the whole subject, he dis- 
covers that the period of rotation of the earth upon its 
axis has not changed by the hundredth part of one 
second of time in a period of more than two thousand 



THE EARTH. 73 

years. We will explain hereafter the train of reasoning 
by which this conclusion has been reached. We shall, 
for the present, accept the statement as a fact. 

The revolution of the earth in its orbit. — In 
the examination already made of the sun's apparent rev- 
olution among the fixed stars, we have found that the 
revolution was performed in the same plane, cutting out 
of the sphere of the fixed stars an exact great circle. 
All that was then affirmed, with reference to the sun's 
apparent motion, must now be affirmed as belonging to 
the earth's real motion. 

The earth, then, revolves around the sun in the plane 
of the ecliptic, at a mean distance of about ninety-jive 
millions of miles, and in a period of about three hundred 
and sixty-five days and a quarter. It, of course, always 
occupies a position distant from the sun's place one half 
a circumference, or one hundred and eighty degrees. The 
changes of the sun's position at noon in the course of the 
year, which we have already examined, are now readily 
accounted for by the fact that the earth's axis of rotation 
neither coincides with the plane of the ecliptic nor is 
perpendicular to it, but is inclined under an angle, which 
is readily measured, and which is found to undergo a 
very slow change from century to century. In case the 
earth's axis were perpendicular to the plane of the 
ecliptic, then the illuminated hemisphere of the earth 
would always be bounded by a meridian circle, and every 
inhabitant of the earth would find his days and nights 
precisely equal, no matter what his location upon the 
earth's surface. If, on the contrary, the axis of the earth 
laid on the plane of the orbit, and remained ever parallel 
to itself, then the illuminated hemisphere would be 
bounded by a great circle, whose diameter would always 



74 THE EARTH. 

be perpendicular to the earth's axis, and an equality of 
day and night would only occur when the earth held such 
a position that its axis would be perpendicular to the line 
joining the earth's center with the sun. Neither of 
these cases exists in nature, and, as we have already 
seen, the annual sweep of the sun from north to south, 
and from south to north, measures the double inclination 
of the earth's equator to the plane of the ecliptic, while 
the length of the day, as compared with the night, com- 
bined with the inclination of the solar beams, produces 
the alternation and changes of the seasons. 

To an inhabitant of the earth's equator, the poles of 
the heavens will ever appear to lie in the horizon, and 
while the sun sweeps, during the year, from south to 
north, and returns, yet the days and nights are ever 
equal, and a perpetual summer reigns around the equa- 
torial region, and a belt of extraordinary heat encircles 
the earth. Could an observer reach either pole of the 
earth, then the pole of the heavens would occupy his 
zenith, all diurnal circles would be parallel to the horizon, 
which would now coincide with the equator, and so long 
as the sun was south of the equator, (the observer being 
at the north pole of the earth), just so long would the 
sun be below the horizon, and every part of its diurnal 
circle would be invisible. On the day of the vernal 
equinox the sun would just reach the equator (now the 
horizon), and during the entire revolution would be seen 
sweeping round the horizon, slowly rising above it. This 
increase of elevation must now progress up to the summer 
solstice, and then decline to the autumnal equinox. The 
daylight thus continuing for six entire months, and the 
darkness for an equal length of time. These theoretic 
statements are abundantly verified by the facts, as re- 



THE EARTH. 75 

ported by those who have visited high northern or south- 
ern latitudes. 

Our climates are, then, undoubtedly, determined by 
the inclination of the earth's axis to the ecliptic, or what 
amounts to the same thing, by the inclination of the 
earth's equator to the ecliptic, the one angle being the 
complement of the other, or what it lacks of being ninety 
degrees. 

The process employed by the ancients in measuring 
the inclination of the equator and ecliptic we have ex- 
plained (chap. I.), and the same, with certain refine- 
ments, is still used by the moderns. At the beginning 
of the present century, this angle, called the obliquity 
of the ecliptic, amounted to 23° 27' 5§." 5. Two hun- 
dred and thirty years before Christ, the same angle, 
measured by the Greek astronomer, Eratosthenes, was 
23.°51 / .20/ / After a lapse of 370 years, Ptolemy found 
the inclination to be 23°.48'.45 // . In the year 880 of 
our era, it was 23°.35 / .00 // . In 1690, Flamsteed found 
the same angle to be 23°.29'.00", and thus from century 
to century the change progresses, reaching, however, a 
limit beyond which it cannot pass, (as we shall presently 
show), when it will commence a reverse motion, and thus 
the one plane slowly rocks to and fro upon the other in a 
calculable, but (so far as I know), not yet calculated 
period. 

The time elapsing from the moment the earth is near- 
est the sun, until it returns again to the same point, is 
called an annomalistic year. The time from vernal 
equinox to the same again, is called a, tropical year, 
while the time occupied by the earth in passing from any 
one point of its orbit, regarded as fixed, to the same point 
again, is called a sidereal year. These different periods. 



76 THE EARTH. 

at the commencement of the current century, had the 
following values : — 

Mean Annomalistic Tear, in solar days, . . . 365.2595981 
" Tropical " " ... 365.2422414 

11 Sidereal " "... 365,2563612 

These figures being different, demonstrate the great 
and important fact that, whatever be the precise figure 
of the curve of the earth's orbit, the point of nearest ap- 
proach to the sun, called the perihelion, is itself in mo- 
tion. The same is true of the vernal equinox, the first 
evidently advancing, the second as evidently retrograding, 
and thus while the advance of the perihelion increases the 
length of the annomalistic year over the sidereal, the retro- 
gression of the equinox decreases the length of the tropi- 
cal, as compared with the sidereal year. 

These figures are presented as the result of the best 
determinations which have been reached in modern times ; 
but it must not be understood that the existence of these 
three different kinds of year are the discovery of our own 
times. The discovery of the motion of the vernal equinox, 
as we have seen, seems to reach back to the highest an- 
tiquity, and was known to all the ancient nations. The 
rate of motion was more exactly determined by the Greek 
astronomers, and hence the discovery has been attributed 
to that nation. Modern observations have confirmed this 
ancient discovery, while modern physical science has 
rendered a satisfactory account of this remarkable pheno- 
menon, and has determined that the equinoctial point 
completes the entire circuit of the heavens in 25,868 
years. 

To ascertain the condition of the perihelion point as to 
rest or motion, it is only necessary to determine the sun's 
place among the fixed stars at the time of any perihelion, 



THE EARTH. 77 

and to transmit the same to posterity. Any change of 
the sun's place among the stars at perihelion, which may 
become known in future ages, will demonstrate the fact 
that the perihelion is not only in motion, but will exhibit 
also the direction of the motion, and the rate of advance 
or recess. By a comparison of ancient observations with 
modern, the perihelion point of the earth's orbit is found 
to be slowly advancing, while, as we have stated above, 
the vernal equinox is slowly retrograding, at such rates 
that these two points pass each other once in 20,984 
years. The perihelion coincided with the vernal equinox, 
as we are able to compute from their relative motions, 
4,089 years before the Christian era. Sweeping onward 
to meet the summer solstice, the perihelion passed that 
point in the year twelve hundred and fifty of our era, 
and will meet the autumnal equinox about the year six 
thousand four hundred and eighty-three. 

From the uniform rotation of the earth on its axis 
we obtain, as already stated, our unit of time. But this 
rotation is not sensible to man except by its effect on the 
position of objects external to the earth ; and hence we 
determine the absolute period of rotation from marking, 
the moment when a fixed object, such as a star, passes 
the meridian of any given place. The time elapsing from 
this moment up to the next passage of the same object 
across the meridian, supposing the earth to be immovable 
as to its central point, would be the exact measure of 
the period of rotation of the earth on its axis. Now, the 
earth's center, in the space of one day and night, or dur- 
ing one rotation, actually passes over nearly 2,000,000 
of miles, and it would seem as though this change of 
position would sensibly affect the return of our star to the 
meridian, but such is tho vast distance of the fixed stars 



78 THE EARTH. 

that visual rays sent to the same star, from the extremi- 
ties of a base line of 2,000,000 miles in length, are ab- 
solutely parallel under the most searching instrumental 
scrutiny that man has been able to make. A sidereal 
day — the time which elapses between the consecutive re- 
turns of the same fixed star to any given meridian — is an 
invariable unit of time, and, as such, is extensively used 
in practical astronomy; but in civil life, inasmuch as 
all the duties of life are regulated by the return of the 
sun to the meridian, sola?*, and not sidereal time, has be- 
come the great standard in the record of all historic 
and chronologic events. In case the earth did not re- 
volve upon its axis, and had no motion except that of 
revolution in its orbit around the sun, it is manifest that 
in the course of one revolution the earth's axis, remaining 
parallel to itself, the circle dividing the illuminated from 
the dark hemisphere of earth would take up successively 
every possible position consistent with its always remain- 
ing perpendicular to the line joining the centers of the 
earth and sun. It is manifest, therefore, that by this 
revolution around the sun this luminary would be caused 
to rise above the horizon of any and every place upon the 
earth's surface successively, slowly to sweep across the 
heavens, and at the end of six months again to sink be- 
neath the horizon. If, then, we define a solar day to be 
the time which elapses from the passage of the sun's 
center across any given meridian until it returns to the 
same meridian again, one such day would evidently be 
produced by the revolution of the earth in its orbit; 
hence we find a solar day to be longer than a sidereal 
day, because of the fact that the sun's center is brought 
to the meridian later, in consequence of its own ap- 
parent motion. Indeed, when we come to examine care- 



THE EARTH. 79 

fully the length of the solar day, we find it to be in a 
state of comparatively rapid change, a fact which we could 
readily have anticipated, as we know the apparent move- 
ment of the sun in its orbit, or rather the real motion 
of the earth, is changing from day to day. When the 
earth is in perihelion, or nearest the sun, it then travels 
with its greatest velocity, and passes over an arc of 
1° 01/ 9". 9, in a mean solar day, whereas, when the 
earth is in aphelion, or furthest from the sun, it sweeps 
over an arc, in the same time, of only 57' ll". 5. We 
thus perceive that the length of a true solar day must 
vary throughout the year, and for the purpose of obtain- 
ing a standard of time the world has adopted what is 
called a mean solar day, or a day having the average 
length of all the true solar days in the year. All the 
time-keepers employed in civil life, such as clocks and 
chronometers, are regulated to keep mean solar time, 
while, for the purposes of an observatory, sidereal time 
is in general use. This, however, is slightly different 
from the sidereal time already defined. The sidereal 
clock of the observatory, if perfectly true, would mark 
Oh. 00m. 00s. at the moment the vernal equinox is on the 
meridian of the observatory. It would mark the same at 
the next return, and hence this sidereal day is really a 
vernal equinox day. Now, as the sun's center appears 
to sweep round the whole heavens in the space of one 
year, and by virtue of this motion passes across the meri- 
dian of any place and returns to the same again, SO, as 
we have seen, the vernal equinox sweeps around the 
heavens in a period of 25,868 years, and thus passes from 
one meridian to the same by virtue of this motion. Thus, 
a vernal equinox day is shorter than a sidereal day 
by an amount equal to one day in 25,808 years, a 



80 THE MOON. 

quantity very minute indeed, but still insisted upon, as 
we desire to impress upon the mind of the reader the dif- 
ferences between these various measures of time. 

The moon a satellite of the earth. — In prose- 
cuting our plan of investigation we must now give some 
account of the moon, as she forms, astronomically speak- 
ing, a part of the planet which we call the earth, and we 
shall find hereafter that when we speak of the orbit, in 
which the earth revolves about the sun, the real point 
tracing that orbit is not the center of the earth, but a 
point determined by taking into consideration the fact 
that the earth and moon must be combined, as forming a 
sort of compound planet, revolving about the sun. Of 
all the celestial orbs furnishing objects for the investiga- 
tion to man no one of them can rival the moon in the 
antiquity of its researches or in the importance and com- 
plexity of its revolutions. 

If it were possible to trace the history of astronomical 
discovery, it would be found, beyond a doubt, that the 
first positive fact ever revealed to the student of the skies 
was the motion of the moon among the fixed stars. This 
fact is so obvious that any one who chooses to mark the 
moon's place by the stars which surround her to-night, 
and compare it with her place on to-morrow night, will 
make for himself the great discovery that the moon is 
sweeping around the heavens in a direction contrary to 
that of the diurnal revolution of the celestial sphere. 
Thus, if we mark the place of the new moon, in the 
evening twilight, when she appears as a silver crescent, 
emerging from the sun's beams, and just visible above the 
western horizon, we shall find that on the next evening, 
at the same hour, her distance from the horizon will have 
been greatly increased, and this increase of distance pro- 



THEMOON. 81 

gresses from night to night, until we find the moon actu- 
ally rising in the east at the time the sun is setting in 
the west. On the following night, at sunset, the moon 
will not have risen, but we will be compelled to wait 
nearly an hour after sunset before she becomes visible 
above the eastern horizon, and thus she advances in her 
orderly march among the fixed stars, until she circles 
entirely around the heavens, passes through the solar 
beams, and reappears in the west above the sun, as a slen- 
der crescent. 

The moon's ee volution in her orbit. — We have 
already stated that, in case it were possible for the sun's 
center to trace out in its revolution among the fixed stars 
a line of golden light, visible to the eye of man, this line 
would be a regular circle, perfected at the close of one 
revolution, and ever after repeated, along the same 
identical track. Such, however, is not the case with 
our satellite. Could the moon's course be traced by 
leaving behind her among the stars a silver thread of 
light, at the completion of one revolution, this thread 
would not join on the point of beginning, but would bo 
more or less remote, and the track described in the 
second and successive revolutions would not coincide 
with that first described ; and thus we should find a 
multiplicity of silver lines sweeping round the circuit of 
the heavens, crossing each other, and interlacing in the 
most complicated manner, and thus making a girdle, or 
zone, of definite width, beyond whose limits the moon 
could never pass. The time occupied in completing one 
of these revolutions from a given star, until it returns to 
the great circle of the heavens, passing through the axis 
and this star again, is soon found to be variable, within 
certain narrow limits. This is called a sidereal revolu- 



82 THE MOON. 

don, and its mean value, at the beginning of the present 
century, is fixed at 27d. 7h. 43m. 11.5s. The most 
obvious lunar period, however, and that doubtless first 
discovered, is that called a synodical revolution, and is 
the period elapsing from the occurrence of full moon to 
full moon again, or from new moon to new moon again. 
The average length of this period, which is also called a 
mean lunation, amounted, at the epoch above mentioned, 
to 29d. 12h. 44m. 2s. 87. It is within the limits of this 
period that the moon passes through all those appearances 
which we call 

The moon's phases. — These extraordinary changes in 
the physical aspect of the moon must have perplexed the 
early astronomers. While the sun ever remained round 
and full-orbed in all his positions among the fixed stars, 
and while all the planets and bright star3 shone with a 
nearly invariable light, the moon passed from a state of 
actual invisibility to a condition in which her disk was 
as round as that of the sun, and thence gradually losing 
her light, finally faded from the eye as she approached 
the solar orb. It was soon discovered that these changes 
were in some way dependent strictly upon the sun, and 
not upon the moon's place among the fixed stars. Any 
one who chooses may verify this discovery, for by locat- 
ing the moon's place among the fixed stars at the full, 
and waiting her return to the same place again, it will 
be found that she has not yet reached her figure of a 
complete circle. Indeed, more than two days are re- 
quired, after passing the position occupied when last full, 
before she gains the point that shall present us with a 
completely illumined disk. The discovery of this truth 
aided undoubtedly in solving the mystery of the moon's 
phases. It was clearly manifest that the moon was re- 



THE MOON. 83 

volving about the earth in an orbit nearly circular. 
This was evident from the fact that the moon's apparent 
diameter did not change, by any sensible amount, dur- 
ing an entire revolution, which would have been impos- 
sible in case her approach to, or recess from the earth, 
had been very great in any part of her orbit. 

Another phenomenon of startling interest aided greatly 
in reaching a true solution of the changes of the moon. 
I refer, of course, to solar and lunar eclipses. We have 
already referred to solar eclipses, as being undoubtedly 
produced by the interposition of the dark body of the 
moon between the eye of the spectator and the sun's disk. 
This demonstrated the fact that the moon in her revolu- 
tion round the earth did sometimes cross the line joining 
the earth's centre with the sun, thus producing a central 
solar eclipse. It was thus manifestly possible for the 
moon's center to cross the same line at a point lying be- 
yond the earth, with reference to the sun. When in this 
position, a straight line drawn through the center of the 
sun, and through the center of the earth, and produced 
onward, would pass through the moon's center, and to a 
person there situated, and looking at the sun, he would 
find the solar surface covered by the round disk of the 
earth, thus producing to the lunarian a solar eclipse. 
When the moon was thus situated, it was found to be 
shorn of a very large proportion of its light, not entirely 
fading from the eye, as did the sun when in total eclipse, 
but remaining indistinctly visible, with a dull reddish 
color. Now, as common observation teaches us that 
every opaque object casts a shadow in a direction oppo- 
site to the source of light, it follows that the earth must 
cast a shadow in a direction opposite to the sun ; and in 
case this shadow reached as far as the moon's orbit, the 



84 THEMOON. 

moon, in taking up her successive positions, would some- 
times pass into the earth's shadow. If self-luminous, the 
passage across the earth's shadow would occasion but a 
trifling change in her appearance. If, however, her 
light was either wholly or in greater part derived from 
the sun, then in passing into the earth's shadow, the 
stream of light from the sun being intercepted by the 
earth, the moon would lose her brilliancy, and could only 
be visible with an obscured lustre. All the phenomena 
presented in a solar as well as a lunar eclipse combine to 
demonstrate that the light of the moon is not inherent, or 
that this orb is not a self-luminous body ■ and all these 
phenomena were perfectly accounted for by admitting 
the hypothesis that the moon shines by reflecting the 
light of the sun. Thus, during a total solar eclipse, 
when the illuminated hemisphere of the moon was turned 
from the earth, her hither side appeared absolutely black, 
while no lunar eclipse ever occurred, except at a time 
when the moon's illuminated hemisphere was wholly vis- 
ible, or at the full moon. In passing from new moon to 
full, it is evident, from the slightest reflection, that as 
the moon slowly recedes from the sun, in her movement 
round the earth, she will turn more and more of her 
illuminated hemisphere towards the earth, the whole of 
which will become visible when she is precisely opposite 
the sun, while the light must decrease in a reverse 
order in passing from the full moon to the new. Thus, 
all the facts and phenomena of ancient as well as of 
modern discovery combine to demonstrate the truth that 
the earth's satellite, like the planets already treated of, 
is only visible by reflecting the light of the sun. 

We are ready by analogy to extend this reasoning to 
embrace the earth, and to believe that our own earth 



THEMOON. 85 

shines to the inhabitants of other planets (if such there 
be), by reflecting the light of the sun. We are not left, 
however, to mere analogy to demonstrate this truth, as 
we have the most positive evidence in the phases of the 
moon that the earth does reflect the solar light. No 
one can have failed to notice the fact that when the moon 
appears as a slender crescent, her entire disk may be 
traced, faintly visible even to the naked eye ; but when 
the telescope is applied, we readily distinguish in this 
darkened part all the outlines and prominent features 
which become visible to the unaided eye when the 
moon is entirely full. This faint luminosity is beyond all 
doubt occasioned by the reflection back again to the earth 
of that light which the earth reflects upon the moon; for 
if we consider the relative positions of the sun, moon, and 
earth, we shall see that at the new moon the whole 
illuminated hemisphere of the earth is turned full upon 
her satellite, and at that time the largest amount of light 
from the earth falls upon the surface of the moon. The 
relative positions of the bodies now slowly change, and as 
the moon increases in light by like degrees, the earth 
loses in light ; and when the moon becomes entirely full, 
the earth will be to the lunarian entirely dark, as her 
non-luminous hemisphere is then turned directly to the 
moon. 

We have already stated that, during a lunar eclipse, 
the moon remains dimly visible. This is not due to the 
reflected light of the sun, thrown upon the moon by the 
earth, but arises from the (act that the solar rays are so 
much bent out of their course in passing through the 
earth's atmosphere, that many of them are still able to 
reach the moon's surface, and thus in some degree to light 
up her disk, even during a central eclipse. 



86 THE MOON. 

Amid all the variations and changes which mark the 
luminosity of the moon one thing remains almost abso- 
lutely invariable. No eye on earth has yet seen more 
than one half of the lunar sphere. The hemisphere 
now visible to man, has (so far as we know.) ever been 
visible, and, except by the intrusion of some foreign 
body, will ever remain turned toward the earth. There 
are slight deviations from the positiveness of this state- 
ment to which we shall have occasion to allude hereafter, 
but the grand truth remains, that the same hemisphere 
of the moon is ever turned toward the earth. 

To account for this remarkable fact we are compelled 
to acknowledge a rotation of the moon on her axis, in 
the exact period employed by her in her revolution in 
her orbit. If the moon had no motion of rotation about 
an axis, then in the course of her orbital revolution 
every portion of her surface would come into view suc- 
cessively. 

This explanation, which it would seem ought to be per- 
fectly satisfactory, has, in some strange way, been not 
only misunderstood, but denied ; and yet should the per- 
son most skeptical undertake to walk round a central ob- 
ject, always turning his face to the center,. without as 
well turning his shoulders and person, he would receive 
a positive conviction of the truth of our explanation of 
a most practical character. 

The physical cause of this remarkable fact in the 
moon's history will be duly considered hereafter. 

The same kind of observation and reasoning which en- 
abled Hipparchus to determine the eccentricity of the 
sun's apparent orbit (the earth's real orbit) sufficed to 
enable this philosopher to determine the eccentricity of 
the moon's orbit, and the epicyclical theory gave a 



THE M N. 87 

tolerably fair account of the most striking irregularities 
in the moon's motion. In one respect, however, we find 
a remarkable difference between the lunar and solar mo- 
tions. The position of the perihelion of the earth's orbit 
moves so slowly that for a period of even a hundred years 
this motion may be neglected without any great error. 
While the moon's apogee, or least distance from the earth, 
was found to be sweeping round the heavens with a com- 
paratively rapid motion, following the moon in her course 
among the stars, so that while in a period of 6,585| days 
the moon performed 241 complete revolutions with refer- 
ence to the stars, she made but 239 revolutions with 
regard to her perigee. Hipparchus succeeded in repre- 
senting this motion by means of eccentrics and epicycles, 
and finally was able to tabulate the moon's places with 
such accuracy as to represent her positions, especially at 
the new and the full) so as to predict roughly solar and 
lunar eclipses. 

Ptolemy discovered, 500 years later, a new irregularity 
in the moon's motion, which reached its maximum value 
in what are called the octants, that is, the points half- 
way between the new moon and her first quarter, and 
so on a quarter of a circumference in advance round 
the orbit. New attempts were made to explain these 
irregularities by a combination of circles and eccentrics. 
It was, finally, approximately accomplished, but all these 
facts thus accumulating were preparing the way for 
the abandonment of an hypothesis which could only be 
maintained by the imperfection of astronomical observa- 
tion. 

The excursions made by the moon, north and south of 
the ecliptic, or plane of the earth's orbit, were obviously 
to be accounted for by the fact that this satellite revolved 



88 THE MOON. 

in a plane, inclined under a certain angle, to the ecliptic. 
This angle was readily measured by the ancients, and, 
though slightly variable, was fixed at the beginning of 
our century at 5° 8' 47 // .9. 

The lunar parallax and distance. — The rude in- 
struments employed by the early observers in their as- 
tronomical observations were insufficient for any delicate 
work, and hence we find them quite ignorant of the 
absolute value of even the moon's parallax, a quantity 
which far exceeds any other parallactic angle of the 
solar system. We have already shown (Chap. I.) how 
the distance of an inaccessible object may be obtained by 
measuring the angles formed at the extremities of a given 
base line, by visual rays drawn to the object. In case 
the base line be very short in proportion to the distance 
to be measured, the sum of the two angles thus measured 
will approach in value 180°, and the angle at the distant 
object formed by the visual rays becomes smaller in pro- 
portion to its distance. In our attempts to measure the 
solar parallax, using the earth's diameter as a base, it 
was found that the delicacy of modern instruments was 
not adequate to so difficult a task. This, however, is not 
the case when we come to apply them in the determina- 
tion of the lunar parallax. Indeed, the moon is found to 
be so near the earth that visual rays, drawn from specta- 
tors at different parts of the earth, not very remote from 
each other, to the moon's center, form with each other 
sensible angles ; and thus the moon, viewed from differ- 
ent stations, is projected among different stars. When 
the moon's center is in the absolute horizon, (that is, in 
a plane passing through the center of the earth and 
perpendicular to the earth's radius drawn to the place 
of the spectator), lines drawn from the center of the 




NORTHWESTERN BOUNDARY OF MARE SERENITATIS 
I860 FEBR.27 8 H. P.M. ALBANY TIME 
DUDLEY OBSERVATORY. 



moon's Cent 
tal para I 
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This, how 
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when the 






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and observe pL iyer agre6j except ^ QI 

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#N BOUNDARY OF MARE SERENITATIS 
FEBR 27 8 H.P^. ALBANY TiMr 
DUDLEY OBSERVATORY. 



THE MOON. 89 

earth and from the eje of the observer unite at the 
moon's center, under an angle called the moon's horizon- 
tal parallax. In case the moon's distance from the 
earth were constant, this angle would also be invariable. 
This, however, is not the case, and we find the horizon- 
tal parallax reaches a maximum value equal to 1° V 24", 
when the moon is nearest the earth, and a minimum 
value of 0°53 / 48," when most remote — the average 
value being 0° 57 7 00".9. These angles give for the 
moon's mean distance from the earth 237,000 miles. 

As all the computed places of the planetary orbs as- 
sume the spectator to occupy the earth's center, we read- 
ily perceive that, in the case of the moon, the computed 
and observed places would never agree, except in one in- 
stance, namely, that in which a line joining the center of 
the earth with the moon's center passes through the place 
of the observer, or when the moon's center is exactly in 
the zenith. The effect of parallax on the apparent place 
of the moon is to sink it below the position it would have 
held in case it were seen from the earth's center. 

Knowing the actual distance of the moon, her real 
diameter is readily determined, and is found to be 
about 2,160 miles ; hence her volume is about one- 
forty-ninth part of that of the earth. We shall have 
occasion hereafter to resume our examination of tho 
moon's motions when we come to discuss the physical 
causes by whose power the planetary orbs are held in 
dynamical equilibrium, and are retained in their orbits. 
We now proceed to examine the physical constitution of 

The moon, as revealed by the telescope. — ■ 
The splendid instruments which modern skill and science 
have furnished for the examination of the distant worlds 
so tar increase the power and reach of human vision, 



90 THE MOON. 

in the case of the moon, as to bring this satellite of the 
earth comparatively within our reach. A telescope 
which bears a magnifying power of one thousand times, 
applied to the examination of the moon's surface, ena- 
bles the observer to approach to within 237 miles of 
this extraordinary world, and even this distance, under 
the most favorable circumstances, may be reduced by 
one-half. This, perhaps, is the nearest approach ever 
made to the moon, and it is at a distance of say 150 
miles that we are permitted to stand and examine at 
our leisure the features which diversify the surface of 
our satellite. No subject has excited so deep an in- 
terest from mere curiosity, as that involved in the actual 
condition of the moon's surface. Every one desires to 
know if the other worlds are like our own. Have they 
oceans and seas, lakes, rivers, islands, and continents ? 
Does their soil resemble our own ? Does vegetable life 
there manifest itself in every variety of grass and flowers, 
and shrub and tree? Are there extended forests and 
spicy groves, filled with multitudinous animals, in these 
far off worlds ? And, above all, are these bright orbs 
inhabited by rational intelligent beings like man ? The 
earnest desire to obtain responses to these and like ques- 
tions, caused to be received, many years since, with the 
most wonderful delight and credulity, a statement put 
forth in America, giving professedly the details of lunar 
discoveries, said to have been made by Sir John Herschel 
at the Cape of Good Hope, in which all these questions 
were most satisfactorily answered. We need hardly say 
how great was the disappointment when these pretended 
discoveries proved to be but fanciful inventions. When 
we call to mind that with a telescope magnifying 2,000 
times we are still separated from the moon 120 miles, we 



THEMOON. 91 

readily perceive the utter impossibility of solving at pres- 
ent, directly by vision, the problem of the moon's habita- 
bility. We know not what may be accomplished by human 
genius and human invention, and after the production of 
so marvellous an instrument as a telescope capable of 
transporting the beholder to within 120 miles of the sur- 
face of a body actually removed 237,000 miles, we will 
not presume to set any specific limits to future effort. 
We can only say that the telescope must become vastly 
improved in its powers of definition and development be- 
fore we can hope to satisfy ourselves, from actual inspec- 
tion, that our satellite is or is not inhabited by a race 
with any of the faculties which distinguish man. 

Let us see what has actually been accomplished by 
telescopic investigation, and although it falls far short- 
of satisfying the curiosity of our nature we shall find 
much to interest and astonish. We can affirm, then, 
that the surface of our satellite is diversified with hill 
and dale, with lofty mountains and mighty cavities, with 
extensive plains and isolated mountain peaks, not very 
unlike the same features presented by our earth. The 
hemisphere of the moon, visible to man, has been studied 
and mapped with the greatest care. Indeed, its eleva- 
tions and depressions have been accurately modeled, the 
mountain elevations have been measured, and the depths 
of the mighty cavities which distinguish her surface have 
all been carefully determined. These measures all de- 
pend on the fact that the moon receives its light from 
the sun, and presents its surface to that orb under ever? 
angle in the courso of its revolution. The mountains of 
the moon, like those of the earth, have their sumniiis 
first lighted by the rays of the rising sun, while all the 
plain beneath, and their rough and rugged sides, are in 



92 THE MOON. 

the deepest darkness. These summits, when so illumin- 
ated, glow and sparkle with a dazzling beauty unsur- 
passed. As the sun rises, we perceive distinctly the 
black shadow of the mountain falling to a great distance 
on the plain below* These shadows slowly decrease 
in length, and their outlines gradually creep up the 
mountain side as the sun reaches the moon's meridian. 
When the sun begins to decline the shadows fall in the 
opposite direction, slowly extend their black masses over 
the distant plains, and darkness finally gathers round the 
mountain sides, till again the summit is alone illumined 
by the rays of a setting sun. It is by means of those 
shadows, whose lengths are readily determined by micro- 
metrical measures, that we are enabled to determine the 
heights of the lunar mountains and the depths of the 
lunar cavities. This process is not more difficult than to 
determine the elevation of a church steeple or other lofty 
object by the length of its shadow cast upon a horizontal 
plane below. The altitude of the sun above the horizon 
at noon will give the direction of the visual ray passing 
from the summit of the object to the extremity of its 
shadow. -Knowing the value of this angle, and the meas- 
ured length of the shadow cast, we have at once the 
means of determining the elevation of the object under 
examination. These simple principles are readily trans- 
ferred to the determination of the heights and depths of 
the lunar surface, while the figure of the shadow cast by 
the summits of a mountain range on an extended plain 
below, gives to us almost as perfect a knowledge of the 
actual forms of the lunar mountains as though it were 
possible actually to tread their lofty summits. 

We find upon the moon's surface a range of mountains 
lifting themselves above a level country and extending 



LUNAR SURFACE 



n 



^m 



#> 







GASSENDIUS, DUDLEY OBSERVATORY 
JAN. I860. 



THE MOON. 93 

nearly two hundred miles, which have received the name 
of the Appenines. This mountain range comes into the 
sunlight just after the moon has passed its first quarter, 
and is then one of the finest objects that the telescope re- 
veals to the eye of man. The brilliancy of the illumin- 
ated heights and ridges, the absolute blackness of the deep, 
rocky chasms, the lofty peaks, the rugged precipices, and 
the deep shadows, all combine to increase the natural 
grandeur of this extensive mountain range. Let it not 
be imagined that details in such a scene, such as actual 
individual rocks, of definite form and outline, are to be 
seen; but as lights and shades produce the forms of 
every surface, so these lights and shadows on the moon 
bring out the absolute forms in the most distinct and per- 
fect manner. The contrasts between the dark and illum- 
inated parts of the moon are far deeper and stronger than 
on the earth. This arises from the fact that the sunlight 
on the moon is not reflected or refracted by an atmosphere 
such as surrounds the earth. The twilight which attends 
the setting sun and the dawn, which so beautifully an- 
nounces the coming of day, does not exist for the lunari- 
ans. If any eye beholds the rising of the mighty orb of 
day from those lofty lunar summits which are first illu- 
mined by his horizontal beams, no gentle flashings, or 
rosy tints, or purple hues, but from intense darkness 
there is an instantaneous burst of brilliant sunlight. The 
beauty of our dawns and twilights is due to the atmos- 
phere which surrounds the earth, and while we cannot 
affirm that no such atmosphere surrounds our satellite, 
we arc certain that whatever gaseous envelope may sur- 
round the moon on its hither side, its density cannot com- 
pare with that of the terrestrial atmosphere. Under very 
favorable circumstances, with the great refractor oi' the 



94 THE MOON. 

Cincinnati Observatory, the author has either seen, or 
fancied he saw, a faint penumbra edging the dark moun- 
tain shadows, and clinging to the black outline, as it 
slowly crept up the mountain side, as the sun rose higher 
and higher. We shall return to this subject when we 
come to treat of certain peculiarities attending the eclipse 
of the sun, and the occultation of stars by the moon. 

Some of the mountains of the moon reach an elevation 
of 8 to 10,000 feet above the general level. Here and 
there we find insulated peaks rising abruptly from ex- 
tended plains to a height of 6 or 7,000 feet, and in the 
early lunar morning flinging their long, sharp, black 
shadows to a vast distance. 

But the most remarkable feature presented in the lu- 
nar surface is the tremendous depths of some of the cavi- 
ties, and their immense magnitude. Some of them ex- 
tend beneath the general level of the country to a depth 
of 10 to 17,000 feet, and their rough, misshapen, precipi- 
tous sides, exhibit scenes of rugged sublimity to which 
earth presents no parallel. Of these cup-shaped cavities, 
especially in the southern portion of the lunar hemisphere, 
the number is beyond credibility ; and, in case we ad- 
mit them to be the extinct craters of once active volca- 
noes, we are forced to the conclusion that convulsions, 
such as the earth is a stranger to, have shaken the outer 
crust of our satellite into a hideousness of form unknown 
in any region of our planet. Some of these deep cavities 
are nearly circular in figure, and with diameters of all 
magnitudes up to twenty miles. Very often the in- 
terior will exhibit a uniformly shaded surface, and in 
the center a conical mountain will lift itself far above this 
level plain. That these convulsions are of different ages 
is clearly manifest from the fact that their outlines very 



THE MOON. 95 

often overlap one another, and the oldest and the newest 
formations are thus distinctly traced by the eye of man. 
So sharp and positive is the outline of these extraordinary 
objects that one cannot but feel that some sudden burst- 
ing forth might even occur while under telescopic exam- 
ination. Once indeed, while closely inspecting these 
seemingly volcanic mountains and craters of the moon, I 
was startled by a spectacle which, for a moment, produced 
upon the mind a most strange sensation. A mighty 
bird, huge in outline and vast in its proportions, suddenly 
lifted itself above the moon's horizon and slowly ascended 
in its flight towards the moon's center. It was no lunar 
bird, however, but one of earth, high up in the heavens, 
winging its solitary flight in the dead of night, and by 
chance crossing the field of vision and the lunar disk. 

Before the power of the telescope had reached its pres- 
ent condition of perfection the darker spots of the moon 
were assumed to be seas and oceans ; but the power now 
applied to the moon demonstrates that there cannot exist 
at this time any considerable body of water on the hemi- 
sphere visible from the earth. And yet we find objects 
such, that in case we were gazing upon the earth from 
the moon, possessing our actual knowledge of the earth's 
lakes and rivers, we should pronounce them, without 
hesitation, lakes and rivers. There is one such object 
which I will describe as often seen through the Cincinnati 
Refractor. The outline is nearly circular, with a lofty 
range of hills on the western and south-western sides. 
This range gradually sinks in the east, and a beautiful 
sloping beach seems to extend down to the level surface 
of the inclosed lake (as we shall call it, for want of other 
language). With the highest telescopic power, under 
the most favorable circumstances, 1 never could detect 



96 THE MOON. 

the slightest irregularity in the shading of the surface of 
the lake. Had the cavity been filled with quick-silver 
and suddenly congealed or covered with solid ice, with a 
covering of pure snow, the shading could not be more 
regular than it is. To add, however, to the terrene like- 
ness, into this seeming lake there flows what looks exactly 
as a river should at such a distance. That there is an 
indentation in the surface, exactly like the bed of a river, 
extending into the country, (with numerous islands,) for 
more than a hundred miles, and then forking and sepa- 
rating into two distinct branches, each of which pursues 
a serpentine course for from thirty to fifty miles beyond 
the fork, all this is distinctly visible. I may say, indeed, 
that just before entering the lunar lake this lunar river 
is found to disappear from sight, and seems to pass be- 
neath the range of hills which border the lake. The re- 
gion of country which lies between the forks or branches 
of this seeming river, is evidently higher, and to the eye 
appears just as it should do, so as to shed its water into 
the stream which appears to flow in the valley below. 
The question may be asked, why is this not a lake and a 
river? There is no lunar atmosphere on the visible 
hemisphere of the moon, such as surrounds the earth, and 
if there were water like ours on the moon, it would be 
soon evaporated, and would produce a kind of vaporous 
atmosphere, which ought to be shown in some of the 
many phenomena involving the moon, but has not yet 
been detected. What, then, shall we call the objects de- 
scribed ? I can only answer that this phenomenon, with 
many other, presented by the lunar surface, has thus far 
baffled the most diligent and persevering efforts to ex- 
plain. In some of these cavities, where the tinting of 
the level surface is so perfect with an ordinary telescope, 



THE MOON. 97 

when examined with instruments of the highest power, 
we detect small depressions in this very surface, cup- 
shaped, and in all respects resembling the form and fea- 
tures of the principal cavity. These hollow places are 
clearly marked by the shadows cast on the interior of the 
edges, which change as the sun changes, and seem to 
demonstrate that these level surfaces do not belong to a 
fluid but to a solid substance. 

Among what are called the volcanic mountains of the 
moon are found objects of special interest. One of them, 
named Copernicus, and situated not far from the moon's 
equator, is so distinctly shown by the telescope, that the 
external surface of the surrounding mountains presents the 
very appearance we would expect to find, in mountains 
formed by the ejecting from the crater, of immense quan- 
tities of lava and melted matter, solidifying as it poured 
down the mountain side, and marking the entire external 
surface with short ridges and deep gullies, all radiating 
from a common center. Can these be, indeed, the over- 
flowing of once active volcanoes? Sir William Her- 
schel once entertained the opinion that they were, and, 
with his great reflecting telescope, at one time discovered 
what he believed to be the flames of an active volcano 
on the dark part of the new moon. More powerful in- 
struments have not confirmed this discovery, and although 
a like appearance of a sort of luminous or brilliant spot, 
has been seen by more than one person, it is almost im- 
possible to assert the luminosity to be due to a volcano in 
a state of irruption, but is more commonly supposed to be 
some highly reflective surface of short extent, and Tor a 
time favorably situated to throw back to us the earth- 
shine of our own planet. 

From some of these seeming volcanoes there are streaky 



98 THE MOON. 

radiations or bright lines, running from a common center, 
and extending sometimes to great distances. These have 
by some been considered to be hardened lava streams of 
great reflective power, but, unfortunately for this hypo- 
thesis, they hold their way unbroken across deep valleys 
and abrupt depressions, which no molten matter flowing 
as lava does, could possibly do. To me they more re- 
semble immense upheavals, forming elevated ridges of a 
reflecting power greater than that of the surrounding 
country. 

We find on the level surfaces a few very direct cuts, as 
they may be called, not unlike those made on our planet 
for railway tracks, only on a gigantic scale, being more 
than a thousand yards in width, and extending in some 
instances over a hundred miles in length. What these 
may be it is useless to conjecture. We cannot regard 
them as the work of sentient beings, and must rather 
consider them as abrupt depressions or faults in the lunar 
geography. 

The moon's center oe figure. — The wonderful 
phenomena presented to the eye on the visible hemisphere 
of the moon have been rendered in some degree expli- 
cable by a remarkable discovery recently made, that the 
center of gravity of the moon does not coincide with the 
center of figure. This is not the place to explain how 
this fact has been ascertained. It is now introduced to 
present its effect, on the hither portion of the lunar orb. 

If the material composing the moon was lighter in one 
hemisphere than the other, it is manifest that the center 
of gravity would fall in the heavier half of the globe. 
For instance, a globe composed partly of lead and partly 
of wood could not have the center of gravity coincident 
with the center of the globe ; but it would lie somewhere 



THE MOON. 99 

in the leaden hemisphere. So it now appears that the 
center of gravity of the moon is more than 33 miles from 
the center of figure, and that this center of gravity falls 
in the remote hemisphere, which can never be seen by 
mortal eye. 

Now, the center of gravity, is the center to which all 
heavy bodies gravitate. About it as a center the lunar 
ocean and the lunar atmosphere, in case such exist, 
would arrange themselves, and the lighter hemisphere 
would rise above the general level, as referred to the 
center of gravity, to an extreme height of 33 miles. 
Admitting this to be true, and as we shall see hereafter 
the fact appears to be well established, we can readily 
perceive that no water, river, lake or sea, should exist 
on the hither side of the moon, and no perceptible atmos- 
phere can exist at so great an elevation. Even vegetable 
life itself could not be maintained on a mountain tower- 
ing up to the enormous height of 33 miles ; and hence 
we ought to expect the hither side of our satellite to pres- 
ent exactly such an appearance as is revealed by tele- 
scopic inspection. 

If the centers of gravity and figure ever coincided in 
the moon, and the change of form has been produced by 
some great convulsion, which has principally expended 
its force in an upheaval of the hither side of the globe, 
then we can account for the rough, broken, and shat- 
tered condition of the visible surface. Lakes and rivers 
may once have existed, active volcanoes might once have 
poured forth their lava streams, while now the dry and 
desolate beds and the extinct craters are only to be 
seen. 

The consequences which How from this singular dis- 
covery as to the figure of our' satellite are certainly very 



100 THE MOON. 

remarkable, and will doubtless be traced with deep interest 
in future examinations. 

Occultations. — As the moon is very near the earth, 
and her disk covers a very considerable surface in the heav- 
ens in her sweep among the fixed stars, she must of course 
cross over a multitude of stars in her revolutions. A star 
thus hidden by the moon is said to be occulted, and these 
occultations are phenomena of special interest on many 
accounts. As a general thing, a star even of the first 
magnitude, in passing under the dark limb of the moon, 
vanishes from the sight instantaneously, as though it 
were suddenly stricken from existence, and at its re- 
appearance its full brilliancy bursts at once on the eye. 
This demonstrates the fact that the stars can be nothing 
more than luminous points to our senses, even when 
grasped by the greatest telescopic power. 

A strange appearance sometimes attends the occupa- 
tion of stars by the moon. The star comes up to the 
moon's limb, entirely vanishes for a moment, then re- 
appears, glides On the bright limb of the moon for a 
second or more, and then suddenly fades from the sight. 

This phenomenon, as also another of most startling 
character attending sometimes the total eclipse of the sun, 
when blood-red streaks in radiations are found to shoot 
suddenly from behind the moon's limb, are supposed by 
some to demonstrate the existence of a lunar atmosphere. 
Much attention has been bestowed on the total eclipses 
of the sun during the past twenty years, for the express 
purpose of solving, if possible, these mysterious radia- 
tions of red light. Some entertain the opinion that they 
are due to the colored glasses used to soften the intense 
solar light, as seen through the telescope. We can only 
say that these phenomena remain without satisfactory 



THE MOON. 101 

explanation, and that the physical condition of the moon 
is yet a problem of the deepest interest. We can assert 
the irregularities of her surface, her deep cavities and 
lofty elevations, her extended plains and abrupt moun- 
tain peaks, but beyond this our positive knowledge does 
not extend. 

We shall resume the consideration of our satellite 
when we come to discuss the great theory of universal 
gravitation. 



CHAPTER V. 



TANCE FROM THE SUN. 



Phenomena of Maes difficult to explain -with the Eakth as the Center 
of Motion. — Copeknican System applied. — Epicycle of Maes. — Betteb 
in6teuments and moee accurate 0.bsebvati0ns. — tycho and kepler. — 
Keplee's method of Investigation. — Ciecles and Epicycles exhausted. 
— The Ellipse. — Its Peopeeties. — The Oebit op Maes an Ellipse. — 
Keplee's Laws. — Elliptical (Debits of the Planets. — The Elements of 
the planetaey orbits explained. — h~ow these elements abe obtained. 
— Keplee's third Law. — Value of this Law. — The Physical Aspect of 
Maes. — Snow Zones. — Potation of the Planet. — Diametee and Vo- 
lume.— Speculation as to its Climate and Coloe. 



This planet is distinguished to the naked eye by its 
brilliant red light, and is one of the planets discovered 
by the ancients. To the old astronomers Mars presented 
an object of special difficulty. Revolving as it does in 
an orbit of great eccentricity, sometimes receding from 
the earth to a vast distance, then approaching so near as 
to rival in brilliancy the large planets, Jupiter and Venus, 
on the old hypothesis of the central position of the earth, 
and the uniform circular motion of the planets, Mars 
presented anomalies in his revolution most difficult of 
explanation. 

These complications were measurably removed by the 
great discovery of Copernicus, which released the earth 
from its false position, and gave to Mars its true center, 
the sun ; but even with this extraordinary advance in the 
direction towards a full solution of the mysterious move- 



MARS. 



103 



ments of this planet, there remained many anomalies of 
motion of a most curious and incomprehensible character. 
It will be remembered that Copernicus, in adopting the 
sun as the center of the planetary orbits, was compelled 
to retain the epicycle of the old Greek theorists, to ac- 
count for the facts which still distinguished the planetary 
revolutions. As in the revolution of the earth about the 




sun there was an approach to and recess from this central 
orb, so in the revolution of Mars it was manifest that 
there was a vast difference between the aphelion and peri- 
helion distances of the planet. The epicycle was then 
retained to account for this anomaly in the motion of 
Mars ; and it will bo readily seen from the figure above 
how this hypothesis rendered a general explanation of the 
facts presented for examination. 



104 MARS. 

The large circle, having the sun for its center, repre- 
sents the orbit of Mars, that is, a circle whose radius is 
equal to the average or mean distance of the planet. 
The small circles represent the epicycle, in the circum- 
ference of which the planet revolves with an equable mo- 
tion, while its center moves uniformly round on the cir- 
cumference of the large circle. When the planet is at A, 
it is in perihelion, or nearest the sun. While the center 
of the epicycle performs a quarter revolution, the planet 
also performs in its epicycle a quarter of a revolution, 
and reaches the position B. A half revolution brings it 
to aphelion in C, and three quarters of a revolution in 
the epicycle locates the planet at D, and an entire revo- 
lution brings it again to A, the point of departure. Thus 
it will be seen that the planet must describe an oval curve, 
traced in the figure A B C D, and for general pur- 
poses this exposition of the phenomena seemed entirely 
satisfactory. It is true that it only accounted for the 
movement from east to west, or in longitude, while the 
motion north and south of the earth's orbit, or in lati- 
tude, was accounted for by supposing the plane of the 
epicycle to vibrate or rock up and down, or right and left 
of the plane of the ecliptic, while its center moved uni- 
formly round in the great circle constituting the orbit of 
the planet. 

So long as observation was so defective as to yield but 
rough places of the heavenly bodies, the deviations from 
the path marked out by the theory of epicycles escaped 
detection. The erection of the great observatory of 
Uraniberg, by the celebrated astronomer Tycho Brahe, 
and the furnishing it with instruments of superior deli- 
cacy, introduced a new era in the history of astronomical 
observation. The instruments employed by Copernicus 



MARS. 105 

were incapable of giving the place of a star or planet with 
a precision such as to avoid errors amounting to even the 
half of one degree, or an amount of space equal to the 
sun's apparent diameter. The instruments employed by 
Tycho reduced the errors of observation from fractions 
of degrees to fractions of minutes of arc, and when thus 
critically examined, the planets, as well as the sun and 
moon, presented anomalies of motion, requiring to ac- 
count for them a large accumulation of complexity in 
the celestial machinery. Such was the condition of 
theoretic and practical astronomy at the era inaugurated 
by the appearance of the celebrated Kepler. This dis- 
tinguished astronomer early became a devoted advocate 
of the Copernican system of the universe, adopting not 
only the central position of the sun, but also the ancient 
doctrine of uniform circular motion, and the theory of 
epicycles. The investigations of Kepler on the motions 
of the planet Mars commenced after joining Tycho at 
Uraniberg, in 1603, and, based upon the accurate observa- 
tions of this later astronomer, finally led to the overthrow 
of the old theory of epicycles and circular motion, intro- 
duced the true figure of the planetary orbits, and with 
the elliptical theory of planetary motion, commenced the 
dawn of that brighter day of modern science, which in 
our age sheds its light upon the world. 

The history of the great discoveries of Kepler presents 
one of the most extraordinary chapters in the science of 
astronomy. It must be remembered that the doctrine of 
circular motion, at once so beautiful and simple, had held 
its sway over the human mind for more than two thou- 
sand years. Such, indeed, was its power of fascination 
that even the bold and independent mind of Copernicus 
could not break away from its sway. When Kepler 



106 MARS. 

commenced his examination of the movements of Mars it 
was under the full and firm conviction that the theory of 
circles and epicycles was unquestionably true. His task, 
then, was simply to frame a combination such as would 
account for the new anomalies in the motions of Mars 
discovered by the refined observations of Tycho. The 
amount of industry, perseverance, sagacity, and invent- 
ive genius displayed by Kepler in this great effort is 
unparalleled in the history of astronomical discovery. 
His plan of operation was admirably laid, and if fully 
and faithfully carried out, could not fail, in the end, to 
exhaust the subject, and to prove at least the great nega- 
tive truth, that no combination of circles and epicycles 
could by any possibility truly represent the exact move- 
ments of this flying world. It is useless to enumerate 
the different hypotheses employed by Kepler. They 
were no less than nineteen in number, each of which 
was examined with the most laborious care, and each of 
which, in succession, he was compelled to reject. Having 
adopted an hypothesis, he computed what ought to be the 
visible positions of the planet Mars, as seen from the 
earth, throughout its entire revolution. He compared 
these computed places or positions with the observed 
places, or those actually occupied by the planet, and 
finding a discrepancy between the two, his hypothesis 
was thus shown to be false and defective, and must neces- 
sarily be rejected. 

It is curious to note the limits of accuracy in the ob- 
served places of the planet, upon which Kepler relied with 
so much confidence in this bold investigation. Many of 
the various hypotheses which he worked up and applied 
with so much diligence, enabled him to follow the planet 
in its entire revolution around the sun, with discrepancies 



MARS. 107 

between observation and computation not exceeding the 
tenth part of the moon's diameter. Indeed, the whole 
error in the computed place of Mars, when compared 
with its observed place, when Kepler commenced the 
problem, did not exceed eight minutes of arc, or about 
one-fourth of the moon's apparent diameter, and yet upon 
this slender basis this wonderful man declared that he 
would reconstruct the entire science of the heavens. 

Having thus framed one hypothesis after another, each 
of which was in its turn rigorously computed, applied 
and rejected, this exhaustive process finally brought 
Kepler to the conclusion that no combination of circles, 
with circular motion, could render a satisfactory account 
of the anomalies presented in the revolution of Mars ; 
and he thus rose to the grand truth, that the circle, with 
all its beauty, simplicity, and fascination, must be banished 
from the heavens. 

The demonstration of this great negative truth was a 
necessary preliminary to the discovery of the true orbit 
in which Mars performed his revolution around the sun. 
Complexity having been exhausted in the combination 
of circles without success, Kepler determined to return 
to primitive simplicity and endeavor to find some one 
curve which might prove to be that described by the 
planet. In tracing up the movement of Mars, as we 
have seen, the figure of the true orbit was evidently an 
oval, and among ovals there is a curve known to geome- 
tricians by the name of the ellipse. This curve is sym- 
metrical in form, and enjoys some peculiar properties 
which we will exhibit to the eye. 

The line A 1> is called the major axis, and is the 
Longest line which can be drawn inside the curve. It 
passes from one vertex A to the other vertex at B, and 



108 



MAKS. 



the semi-ellipse A D B is such that if turned round the 
axis A B, it would fall on, and exactly coincide with the 
semi-ellipse, A C B. The line C D is called the manor 
axis, and is the shortest line which can he drawn in the 
ellipse. This line divides the figure into two equal por- 
tions, exactly symmetrical. 

C 




The point L is called the center of the ellipse, and di- 
vides all the lines drawn through it and terminating in 
the curve into two equal parts. But there are two 
points, and 0', called the foci, which enjoy very pe- 
culiar properties. If from C as a center, and with a 
radius equal to A L, the semi-major axis, we describe an 
arc, it will cut the major axis in and 0', the two foci. 
Now, in case we assume any point on the curve as P, 
and join it with and O', the sum of these lines, P 
and 0' P, will be equal to the major axis, A B. 

Such are the distinguishing properties of the curve, 
which holds the next rank in order of beauty, simplicity, 
and regularity, after the circle. While the circle has 
one central point, from which all lines drawn to the curve 
are equal, the ellipse has two foci, from which lines 



MARS. 109 

drawn to the same point on the curve, when added to- 
gether, are equal in length to the major axis. When 
the major axis of the ellipse is assumed as the diameter 
of a circle, the circumference will wholly inclose the 
ellipse. When the minor axis is assumed as the diame- 
ter, the circumference will lie wholly within the ellipse. 
When the foci, and 0', are very near the center, then 
these circles, and the ellipse lying between them, are very 
close to each other. 

When Kepler was compelled to abandon the circle and 
circular motion as a means of representing the planetary 
revolutions, he adopted the ellipse as the probable form 
of the orbits of these revolving worlds, and made an 
especial effort to apply this new figure to a solution of 
the mysteries which still enveloped the motions of Mars. 
But here a new difficulty presented itself. In the circu- 
lar orbits and epicycles a uniform motion was always 
accepted, but in the ellipse, every point of which is at 
unequal distances from the focus, some law of velocity 
had to be discovered to render it possible to compute the 
planet's place, even after the axis of the ellipse had 
been determined. Here again was opened up to the 
mind of the laborious philosopher a wide field of investi- 
gation. Many were the hypotheses which he framed, 
computed, applied and rejected, but finally fixing the 
sun in the focus of the assumed elliptic orbit, and as- 
suming that the line drawn from the sun's center to 
the planet would sweep over equal amounts of area in 
equal times, he computed the places of Mars through an 
entire revolution. These newly computed places were 
now compared with those actually filled bv the revolving 
world, and Kepler found to his infinite delight that the 
planet swept over the precise track which his hypothesis 



110 MARS. 

had enabled him to predict, and with an exultation of 
victorious triumph to which the history of pure thought 
furnishes few parallels, Kepler announced to the world 
his two first laws of planetary motion, which may be 
given as follows : — 

1. Every planet revolves in an elliptical orbit about 
the sun, which occupies the focus. 

2. The velocity of the planet on every point of its 
orbit is such that the line drawn from the sun to the 
planet will sweep over equal areas in equal times. 

At the time Kepler lived, human genius could not 
have won a grander triumph, for it was not only a 
triumph over nature, which compelled her to render up 
her inscrutable secrets, but a triumph which for ever 
freed the mind from the iron sway of the schools, and 
from the prejudices which had become venerable with the 
lapse of more than twenty centuries of unyielding power. 
No grander emotions ever swelled the human heart than 
those which Kepler experienced when, tracing this fiery 
world through his sweep among the fixed stars, he found 
he had truly and firmly bound his now captive planet in 
chains of adamant, from which in all future ages it could 
never escape, having fixed for all time the figure of the 
orbit and the law of its orbital velocity. This extended 
notice is due to the well merited fame of Kepler, as well 
as to the grandeur of the laws discovered. 

The elliptical theory, now successfully applied to the 
planet Mars, was extended rapidly to Mercury, to the 
moon, and in order to all the known planets. We shall 
hereafter, in our treatment of the planets, adopt the el- 
liptical theory, and to render our language entirely intel- 
ligible, will proceed to explain what is meant by the ele- 
ments of the orbit of a planet. 



MARS. Ill 

To determine the magnitude of any ellipse, we must 
know the longer and shorter axis, or the longer axis and 
the distance from the center to the focus, called the eccen- 
tricity. 

To determine the position of the plane of an ellipse, we 
must know the position of the line of its intersection with 
a given plane, (usually the ecliptic) called the line of 
nodes, and also the angle of inclination with this fixed 
plane. 

To determine the position of the elliptical orbit in its 
own plane, we must know the position of the vertex, or 
extremity of the major axis, called the perihelion. 

And finally, to trace the planet after all these matters 
shall be known as to its orbit, we must know its place 
or position in its orbit at a given moment of time, and 
its period of revolution. 

Now, every plane of every planetary orbit passes 
through the sun's center. 

Every longer axis of every planetary orbit passes 
through the sun's center, and every line of nodes of all 
the planetary orbits passes through the sun's center. 
Thus we have one point of every axis, line of nodes, and 
plane of every orbit of the primary planets. 

To obtain the longer axis we have only to measure the 
planet's distance from the sun when in aphelion and in 
perihelion. These distances added together make the 
longer axis of the orbit. The perihelion distance being 
known, Ave readily obtain the eccentricity, hence the 
Bhorter axis, and from those the entire ellipse in magni- 
tude. The point at which a planet passes from north to 
south of the ecliptic is one point in its line of nodes, the 
sun's center is another, and these determine the direc- 
tion of the line of nodes. The inclination oi' plane ^( the 



112 MARS. 

planet's orbit to the ecliptic is measured by the angle 
formed between a line drawn from the sun's center per- 
pendicular to the line of nodes in the plane of the eclip- 
tic, and one perpendicular to the same line at the same 
point, but lying in the plane of the planet's orbit. The 
elevation therefore of the planet above the ecliptic, when 
90° degrees from the node, will be the angle of inclina- 
tion. Having the line of nodes and inclination, we can 
draw the plane. Having the perihelion point, longer 
axis and eccentricity, we can construct and locate 
the elliptic orbit, and having the moment of perihel- 
ion passage, we can trace the planet in its future move- 
ments. 

The elliptical theory being adopted and extended to all 
the known planets successfully, it became manifest to 
the searching genius of Kepler that there existed too 
many common points of resemblance between these re- 
volving orbs not to involve some common bond which 
united them into a scheme of mutual dependence. They 
all revolved in elliptical orbits. These orbits had one 
common focus, the sun. The lines of nodes and princi- 
pal axes intersected in the sun. They all obeyed the 
same law in their revolution in their orbits, and Kepler 
now undertook the task, almost hopeless in its character, 
of discovering some bond of union which might reduce a 
multitude of now isolated worlds to an orderly and de- 
pendent system. 

This problem occupied the mind of Kepler for no less 
than nineteen years. He examined carefully all the ele- 
ments of the planetary orbits, and finally selected the 
mean distances and periodic times as the objects of his 
special investigation. He found that the periods of re- 
volution increased as the planet was more remote from 



MARS. 113 

the sun, but certainly not in the exact ratio of the dis- 
tance. Thus — 

The mean distance of the earth is . . 95,000,000 of miles. 

Its period of revolution, .... 3 65 \ days. 

Mean distance of Mars, .... 142,000,000 of miles. 

Period of revolution, 687 days. 

In case the distances and periodic times were exactly 
proportional, we should have -V 4 /— ff !• But -W-=1.5 
nearly, while ff 1=1.9 nearly. Finding that no simple 
proportion existed between these quantities, Kepler broke 
away from the ratios of geometry, which up to his own 
era had almost exclusively been employed in all astrono- 
mical investigations, and conceived the idea that the hid- 
den secret might be found in proportions existing between 
some powers of the quantities under consideration. He 
first tried the squares, or simple products of the quanti- 
ties by themselves. Here he was again unsuccessful. 
He now rose yet higher, and examined the relations of 
the cubes of the periods and distances. But no propor- 
tion was found to exist among these third p>owe?*s. At 
length he was led by some influence, he knew not what, as 
he says, to try the relation between the squares of the peri- 
ods and the cubes of the distances, thus, ||f x fff, and 
"W" x ~W _ x -W- 5 an( * h ere l a y th e grand secret, for if any 
one will perform the operations above indicated, and square 
the periods of revolution, and cube the mean distances, 
he will find the above quantities to be equal to each other, 
or, in other language, ho will find the squares of the 
periodic times exactly proportional to the cubes of the 
mean distances. 

This is called the third law of Kepler, and is perhaps 
the grandest and most important of all his wonderful dis- 
coveries. Through its power the worlds are all linked 



114 MARS. 

together. The satellites of the planets revolve in obedi- 
ence to its sway, and even those extraordinary objects, 
the revolving double stars, are subjected to the same con- 
trolling law. It resolves at once the most difficult pro- 
blems involved in the solar system, affording a simple 
method of determining the mean distances of all the 
planets, by measuring the mean distance of any one 
planet, and by observing the periods of revolution. 

As we have already seen, the periodic times are read- 
ily determined from noting the days and fractions of days 
which elapse from the planet's passage through its node 
until it returns to the same node again. This, in case 
the line of nodes remained absolutely fixed, would give 
the time of revolution precisely, and a slight correction 
suffices to correct the error due to the movement of the 
nodes. The determination of the mean distance of the 
earth, then, becomes the key to a knowledge of all the 
planetary distances, from which flows the absolute magni- 
tudes of the planets and their densities. 

It is not, then, surprising that Kepler, seeing the 
grandeur of the consequences flowing from the great dis- 
covery, should have given utterance to his feelings in 
language of the most lofty enthusiasm. 

With the knowledge of the three laws discovered by 
Kepler modern astronomy commenced a career of won- 
derful success. We shall find, hereafter, that even these 
great laws of Kepler are but corollaries to a higher law 
yet remaining to be developed, but we prefer to follow 
out the order of examination and development already 
commenced. 

We resume our discussion of the planet under exami- 
nation. The changes in the apparent diameter of Mars 
must, of course, be very great. When in opposition to 



MARS. AUG.30.8 H.55 M.I845 




MARS, CINCINNATI OBSERVATORY 
AUG 5 TH 1845. 



MARS. 115 

the sun, or on a line joining the sun and earth, Mars is 
only forty-seven millions of miles from our planet, while, 
on reaching his conjunction with the sun, this distance is 
increased by the entire diameter of the earth's orbit, or 
196 millions of miles. When in opposition Mars shines 
with great splendor, presenting to the eye, as shown by 
the telescope, a large and well-defined disk, with a sur- 
face distinctly marked with permanent outlines of what 
have been conjectured to be continents and oceans. The 
polar regions are distinguished by zones of brilliant white 
light, which, in consequence of their disappearance un- 
der the heat of summer, and their reappearance as the 
winter comes on, have been considered as due to snow 
and ice. I have examined these snow zones with the 
great refractor of the Cincinnati Observatory, under 
peculiarly favorable circumstancs. To illustrate the 
mode of observation employed in the determination of the 
period of rotation of Mars on its axis, and the power of 
the telescope in the revelation of the physical constitu- 
tion of this planet, I append some account of Maedler's 
observations, made in 1830, and also of those made at the 
Cincinnati Observatory in 1845 : — 

The last opposition of Mars, which occurred on the 
20th August, 1845, furnished a fine opportunity for the 
inspection of the irregularities of its surface. When in 
opposition the planet rises as the sun sets, and the earth 
and planet are in a straight line, which, by being pro- 
longed, passes through the sun. As the orbit of Mais 
incloses that of the earth, it will be seen from a little re- 
flection that when Mars is in opposition it is nearer to 
the earth than at any other time, nearer than when in 
conjunction by the entire diameter of the earths orbit, 
or 190 millions of miles. In case the orbits of Mars and 



116 MAES. 

the earth were exact circles, the distance between the two 
planets at every opposition would be the same, but the 
elliptic figure of the orbits occasions a considerable varia- 
tion in this distance, and the least distance possible be- 
tween the earth and Mars will be when an opposition oc- 
curs at the time that the earth is furthest from the sun 
and Mars nearest to the sun. Such was approximately 
the relative positions of the planets in 1845, and their 
distance was then less than it can be again for nearly 15 
years. During the opposition which occurred in 1830, 
the earth and Mars held nearly the same relative posi- 
tions. The planet was observed by Dr. Maedler, the pres- 
ent distinguished Director of the Imperial Observatory at 
Dorpat, Russia, assisted by Mr. Beer. I have translated 
the following notices from Schumacher's journal :- — 

" The opposition of Mars which occurred in the month 
of September of this year (1830), and at which time this 
planet approached nearer the earth than it will again for 
15 years, induced us to observe the planet as often as the 
clouds would permit, in order to determine the position 
and figure of its spots ; their possible physical changes, 
and especially the time of revolution on its axis. The 
telescope employed was a Franenhofer Refractor, 4£ feet 
focus. 

" The opposition occurred on the 19th September, and 
the nearest approach to the earth (0,384) on the 14th of 
the same month. In all succeeding oppositions up to 
1845, this distance amounts to 0.5, and even up to 0.65 
(the unit being the mean distance of the earth from the 
sun). On account of the accurate definition of the instru- 
ment, we were able to employ a power of 300 generally, 
and never less than 185. With low magnifying powers, 
the greatest diameter was determined to be a little less 



MARS. 117 

than 22". Our observations extended from the 20th 
September to the 20th October, during which time 17 
nights, more or less favorable, occurred, and all sides of 
Mars came into view. Thirty-five drawings were exe- 
cuted. It was not thought advisable to apply a microme- 
ter, as the thickness of the lines would have produced 
greater errors in such minute measures than those arising 
from a careful estimation by the eye. The drawings 
were invariably made with the aid of the telescope. 
Commonly a little delay was had, till the undetermined 
figure of the spots visible at the first glance separated 
themselves (to the eye) into distinct portions. 

■4k AU 4U ' -it* -it* -ifc Jfe 

'TV *W* TT ,-T^ •TV *F TV 1 

" On the 10th September a spot was seen so sharp 
and well defined, and so near the center of the planet, 
that it was selected to determine the period of rotation. 
On the 14th September it retrograded from the eastern 
hemisphere, through the center to the western hemis- 
phere, in the course of three hours. Its figure un- 
altered during four days, and its regularity as to rota- 
tion left no doubt of its identity and permanence. 

" In the course of 2{ hours Mars exhibited an entirely 
different appearance. The spot (already alluded to) 
was near the western disk of the planet. On the 16th it 
was again observed, and the period of revolution de- 
duced. It was invisible up to the middle of October, ap- 
pearing only in the day time on the side of the planet 
next to tho earth. It was first observed again on the 
19th October, and the disk of Mars showed itself with 
uncommon sharpness. On the southern border of the 
principal spot two red spots were seen, resembling a 
ruddy sky on the earth. They appeared fainter an 
hour after, and although they again seemed brighter 



118 MARS. 

they were never again seen red. We also observed a 
faint spot near the principal one, which was never after 
visible. 

" The observations from the 26th September to the 
5th October showed to us some very dark spots, which 
in zone-formed extensions showed a strong contrast to 
the brightly illuminated surfaces free from spots. A 
fragment of one of these spots was at the north end dis- 
tinct and broad, while at the south end it was so small 
as to be seen with difficulty. Between the pole and the 
principal spot, there was seen a broad stripe, of less 
shade, while the northern hemisphere was almost en- 
tirely free from spots. Bad weather interrupted the ob- 
servations from the 5th to the 12th October. 

" On the 13th, a spot appeared for the first time 
again, but so near the western disk that we recognized 
its return only on the 14th. 

"More accurate observations were had on the 19th 
and 20th October, when this spot passed the middle of 
Mars, which movement was observed with all accuracy, 
and hence a new determination of the period of revolu- 
tion. Computation gave the magnitude of the invisible 
part of Mars on the 13th October=0.06, on the 20th, 
0.08, of the radius of Mars. 

" From the beginning of the observations there was 
seen at the south pole, always with great distinctness, a 
white, glittering, well defined spot, which has long been 
observed, and is called the l snow zone.'' During the 
observations it continually diminished up to the 5th of 
October. Here an increase commenced, yet very slow. 
On the 10th September we estimated it, =.110; 5th 
Oct. = .110, and 20th Oct =.115 of the diameter of Mars. 



MARS. 



119 



" In case we adopt Herschel's determination of inclina- 
tion and position of the axis of Mars, with reference to its 
orbit, the south pole of Mars on the 14th of April, 1830, 
must have had its equinox, and on the 8th September, 
its summer solstice. The smallest diameter of the ' snow 
zone ' occurred on the 27th day after the summer sol- 
stice, a time which corresponds to the last half of July 
on the northern hemisphere of the earth, at which time 
it is well known we have the greatest heat. 

" Preceding observers in oppositions, where the pole 
was further from the maximum temperature, have seen 
the ' snow zone ' much larger, although nearly all regard 
it as changeable in size. These facts seem to sustain the 
hypothesis of a covering of snow." 

As a further confirmation of this hypothesis, we sub- 
join the following computations, by the same persons. 
The previous determinations of the elder Herschel are 
taken as the basis of the calculations. This white polar 
region is now distinctly visible, and seems to be accounted 
for in no other way. Comparing the various seasons in 
Mars, Maedler finds as follows : — 



Duration of Spring, N". Hemisphere, 


. 191-J Mars' days. 


" Summer, " . . 


. ISO " 


" Autumn, " . . 


. 149* " 


Winter, « . .. 


. 147 



a Adding spring and summer together, and fall and 
winter, we have — 

11 Duration of Summer in N. II. to S. II, . . . as 19 to 15 
" Intensity of sun's light in N. H. to S. H., . . as 20 to 29 

11 Uniting these two proportions, and assuming that 
heat and light are received in equal ratios, it will follow 
that the south pole, by the greater intensity of solar heat, 
is more than compensated for the shortness of its sum- 



120 MARS. 

mer. But since for the winter the proportion of 20 to 29 
is reversed, so will the winter of the south pole, not only 
on account of longer duration of cold, but also from its 
greater intensity, be far more severe than in the north 
pole. 

" Herewith agree the facts that preceding observers 
have not lost sight of the i snow zone ' of the south pole, 
even when the pole became invisible, whence it follows 
that it must extend from the pole 45° degrees and even 
further, while we, under like circumstances, could not 
discover any such appearance on the north side of Mars. 
On the contrary, the brightness of this portion was exactly 
like that -of the other parts of the disk." 

The conclusions reached by the German astronomers, 
as above, were confirmed in the fullest manner by the 
observations made at the Cincinnati Observatory during 
the opposition of 1845. I will here record some singular 
phenomena connected with the " snow zone," which, so far 
as I know, have not been noticed elsewhere. 

On the night of July 12th, 1845, this bright polar 
spot presented an appearance never exhibited at any pre- 
ceding or succeeding observation. In the very center of 
the white surface was a dark spot, which retained its 
position during several hours, and was distinctly seen by 
two friends, who passed the night with me in the observa- 
tory. It was much darker and better defined than any 
spot previously or subsequently observed here, and, in- 
deed, after an examination of more than eighty drawings 
of the surface of this planet by other observers at previ- 
ous oppositions, I find no notice of a dark spot ever hav- 
ing been seen in the bright snow zone. On the following 
evening no trace of a dark spot was to be seen, and it has 
never after been visible. 



MARS. 121 

Again, on the evening of August 29th, 1845, the snow 
zone, which for several weeks had presented a regular 
outline, nearly circular in appearance, was found to be 
somewhat flattened at the under part, and extended east 
and west so as to show a figure like a rectangle, with its 
corners rounded. On the evening of the 30th August I 
observed, for the first time, a small bright spot, nearly 
or quite round, projecting out of the lower side of the 
polar spot. In the early part of the evening the small 
bright spot seemed to be partly buried in the large one, 
and was in this position at 8h. 55m., when the draw- 
ing, No. 1, was made. After the lapse of an hour or 
more, my attention was again directed to the planet, when 
I was astonished to find a manifest change in the posi- 
tion of this small bright spot. It had apparently sepa- 
rated from the large spot, and the edges of the two were 
now in contact, whereas when first seen they overlapped 
by an amount quite equal to one-third the diameter of 
the small spot. On the following evening I found a re- 
currence of the same phenomena. In the course of a few 
days the small spot gradually faded from the sight and 
was not seen at any subsequent observation. Should 
Herschel's hypothesis be admitted, that the bright zone 
is produced by snow and ice near the. pole of the planet 
analogous to what is known to exist at the poles of the 
earth, these last changes may be accounted for, by sup- 
posing the small bright spot to have been gradually 
dissipated by the heat of the sun's rays. 

Its apparent projection over the boundary of the large 
snow zone may have been merely optical, and the sepa- 
ration may have been occasioned by seeing the two ob- 
jects in such position as to prevent the one from being 
projected on the other. Such change may have been 



122 MARS. 

produced by the rotation of Mars on its axis in the space 
of a few hours. 

To determine the exact period of rotation of Mars, Sir 
William Herschel instituted a series of observations in 
1777, which were followed by others during the opposi- 
tion of 1779. From the first series an approximate 
period of rotation was obtained, and by uniting the ob- 
servations of 1777 and those of 1779, and using 24h. 
39m. as the approximate period of rotation, Herschel 
made a further correction, and fixed the rotation at 24h. 
39m. 21.6s. 

Maedler's determination, in 1830, gave, for a final 
result, 24h. 37m. 10s., which, in 1832, was corrected 
and fixed at 24h. 37m. 23.7s. 

In 1839 Maedler reviewed Herschel's observations, 
from whence his first results were deduced, and discovered 
that after introducing the necessary reduction, the dis- 
crepancy of two minutes might be reduced to two seconds, 
by giving to Mars one more rotation on its axis, between 
the observations of 1777 and 1779, than Herschel had 
employed. 

In 1845, when Mars again occupied the same relative 
position that it had done in 1830, it was too far south 
for observation at Dorpat. 

By combining Maedler's observation, made at Berlin, 
1830, September 14, 12h. 30m., with one made at the 
Cincinnati Observatory, 1845, August 30, 8h. 55m., 
making the corrections due to geocentric longitude, 
phase, and aberration, I find the period of rotation to be 
24h. 37m. 20.6s., differing by only two seconds from 
Maedler's period as last corrected. 

It is generally believed that Mars is surrounded by an 
atmosphere which in many respects resembles our own. 



MARS. 123 

In case this be true, we may anticipate the existence of 
belts of clouds, and occasional cloudy regions, which 
would modify the outline of the great tracts of sea and 
land, and would account for the rapid changes which are 
sometimes noticed in the surface of the planet. 

The axis of the planet is inclined to its orbit (as may 
readily be deduced from the rotation of the spots) under 
an angle of a little more than 30°, hence the variations 
of climate and the changes of season in Mars will not be 
very unlike those which mark the condition of our own 
planet. Indeed, there are many strong points of resem- 
blance in the planetary features of the earth and this 
neighboring world. The planes of their orbits are but 
little inclined to each other, a little less than 2°. Then- 
years are not widely different when we take into account 
the vast periods which distinguish some of the more dis- 
tant planets. 

The seasons ought to be nearly alike, and the length 
of day and night, as determined by the periods of rotation 
of the two worlds, is nearly the same. In case the great 
geographical outlines are alike, and seas and continents 
really diversify the surface of Mars with an atmosphere 
and clouds, the two worlds bear a strong resemblance to 
each other. 

The actual diameter of Mars is only 4,100 miles, or a 
little more than half the diameter of our earth, while its 
volume is not much greater than one- tenth part of the 
volume of our planet. 

To the inhabitants of Mars (if such there be) the earth 
and moon will present a very beautiful pair of indissolu- 
bly united planets, showing all the phases which are 
presented by Mercury and Warns to our eyes, the two 
worlds never parting company, and always remaining at 



124 MARS. 

a distance of about one quarter of one degree, or about 
half the moon's apparent diameter. 

The amount of heat and light received from the sun by 
Mars is about one half of that which falls on the earth ; 
and in case the planet were placed under the identical 
circumstances which obtain on earth, the equatorial 
oceans even would be solid ice. This, we have every rea- 
son to believe, is not the case, and hence we are induced 
to conclude, as in other cases, that the light and heat of 
the sun are subjected to special modifications, by atmo- 
spheric and other causes, at the surfaces of each of the 
worlds dependent on this great central orb. 

The reddish tint which marks the light of Mars has 
been attributed by Sir John Herschel to the prevailing 
color of its soil, while he considers the greenish hue of 
certain tracts to distinguish them as covered with water. 
This is all pure conjecture, based upon analogy and de- 
rived from our knowledge of what exists in our own 
planet. If we did not know of the existence of seas on 
the earth, we could never conjecture or surmise their 
existence in any neighboring world. Under what modi- 
fication of circumstances sentient beings may be placed, 
who inhabit the neighboring worlds it is vain for us to 
imagine. 

It would be most incredible to assert, as some have 
done, that our planet, so small and insignificant in its 
proportions when compared with other planets with which 
it is allied, is the only world in the whole universe filled 
with sentient, rational, and intelligent beings capable of 
comprehending the grand mysteries of the physical uni- 
verse. 



CHAPTER VI. 

THE ASTEROIDS: A GROUP OF SMALL PLANETS, THE 
FIFTH IN THE ORDER OF DISTANCE FROM THE SUN. 

The Interplanetary Spaces. — Kepler's Speculations. — Great Interval be- 
tween Mars and Jupiter.— Bode's Empirical Law.— Conviction that a 
Planet existed between Mars and Jupiter. — Congress of Astronomers. 
— An Association Organized to Search for the Planet. — Discovery of 
Ceres. — Lost in the Solar Beams. — Rediscovered by Gauss.— The New 
Order Disturbed by the Discovery of Pallas.— Oller's Hypothesis. — 
Discovery of Juno and Vesta.— The Search Ceases.— Renewed in 1845. 
— Many Asteroids discovered.— Their Magnitude, Size, and probable 
Number. 

The worlds thus far examined in our progress outward 
from the sun have been known from the earliest ages. 
Those constituting the group under consideration, called 
asteroids, have all been discovered since the commence- 
ment of the present century. 

The circumstances attending the discovery of 

Ceres, ® of the asteroids are replete with interest, 
and demonstrate the power of the conviction in the human 
mind that, in the organization of the physical universe, 
some systematic plan will be found to prevail. In draw- 
ing to a scale the solar scheme of planetary orbits, it was 
readily observed that the distances of the planets from the 
sun increased in a sort of regular order up to the orbit 
of Mars. Here, between Mars and Jupiter, there was 
found a mighty interval, after which the order was re- 
stored as to the planets beyond the orbit of Jupiter. 

As early as the beginning of the seventeenth eentury, 



126 THE ASTEROIDS. 

Kepler, whose singular genius was captivated by mystical 
numbers and curious analogies, conjectured the existence 
of an undiscovered planet in this great space which in- 
tervened between Mars and Jupiter. The thought thus 
thrown out required no less than two hundred years to 
take root and yield its legitimate fruit. The discovery 
of a planet beyond the orbit of Saturn, by Sir William 
Herschel, in 1781, greatly strengthened the opinions 
based on the orderly arrangement of the interplanetary 
spaces ; and the German astronomer, Bode, by the dis- 
covery of a curious relation, which seemed to control 
the distances of the planets, gave additional force and 
power to the conjecture of Kepler. This law is a very 
remarkable one, and although no explanation could be 
given of it, was verified in so many instances as almost 
to force one to the conclusion that it must be a law of 
nature. We present the law in a simple form. Write 
the series- 

0, 3, 6, 12, 24, 48, 96, &o. 
add 4 4 4 4 4 4 4, &c. 

sum 4 7 10 16 28 52 100, &c. 
Now, if ten be taken to represent the distance of the 
earth from the sun, the other terms of the series will 
represent with considerable truth the distances of the 
other planets, as we will readily perceive, thus : — 

Mercury. Yenus. Earth. Mars. Jupiter. Saturn. Uranus. 

4*7 10 16 28 52 100 196 
The true distances are roughly as under : — ■ 

3.8 7.2 10 15.2 52 95.3 191.8 

It is thus seen that the actual distances of the planets 
agree in a most remarkable manner with those obtained 



THE ASTEROIDS. 127 

by the application of Bode's Law, and as no planet was 
yet known to fill the distance (28) between Mars and 
Jupiter, it required very little devotion to the analogies 
of nature to create in any mind a firm belief in the ex- 
istence of an unknown planet. 

The German astronomers, at the close of the last cen- 
tury, took up the matter with earnest enthusiasm, and in 
the year 1800 a congress or convention of astronomers 
was assembled at Lilienthal, of which M. Shroeter was 
elected president, and Baron De Zach perpetual secre- 
tary. It was agreed to commence a systematic search 
for the unknown planet, by dividing the belt of the 
heavens near the sun's path, called the zodiac (and within 
whose limits all the planetary orbits are confined), among 
twenty-four astronomers, who with their telescopes should 
search for the object in question. 

It was manifest that the unknown planet must be 
very small, too small to be visible to the naked eye, 
otherwise its discovery must have been long since accom- 
plished. It might, however, prove to be large enough to 
exhibit a planetary disk in the telescope, in which event 
a simple search was all that was required. If, however, 
it should be too diminutive to show a well defined disk in 
the telescope, then another method of examination would 
be required. The planet could only be detected by its 
motion among the fixed stars. This, indeed, is the way 
in which all the old planets had been discovered ; but 
while the naked eye takes in at the same time a large 
portion of the celestial sphere, the telescope is extremely 
limited in its field of view, rendering the search labor- 
ious and difficult. Were it possible, however, to make an 
exact chart of all the stars in a given region of the heav- 
ens, to-night, if an examination on to-morrow night of 



128 THE ASTEROIDS. 

the same region should show a strange star among those 
already charted, this stranger might with some proba- 
bility be assumed to be a planet. 

A few hours of patient watching would show whether 
it was in motion, and a few nights of observation would 
reveal its rate of motion. 

Such was the mode of research adopted by the society 
of planet-hunters. The system thus adopted had not 
been pursued but a few months when a most signal suc- 
cess crowned the effort. On the night of the 1st January, 
1801, Piazzi, of Palermo, in Sicily, observed a star in 
the constellation Taurus, which he suspected to be a 
stranger. On the following night (having fixed its posi- 
tion anew with reference to the surrounding stars), he 
found it had changed its place by an amount so large 
that its real motion could not be doubted. The star 
was found to be retrograding, or moving backward, and 
this continued up to the 12th January, when it became 
stationary. It was soon after lost in the rays of the sun, 
thus becoming invisible, before any considerable portion 
of its orbit had been observed, and before Piazzi could 
communicate his discovery to any member of the society. 

Piazzi not considering it possible that a planet which 
had remained hidden from mortal vision from its crea- 
tion could be discovered with so little effort as had thus 
far been put forth, conceived that the moving body which 
he had discovered was a comet, but the intelligence hav- 
ing been communicated to the society, Bode promptly 
pronounced this to be the long sought planet, an opinion in 
which he was sustained by Olbers and Buckhardt, Baron 
de Zach, and Gauss, and I know not by how many other 
members of the society. 

It now became a matter of the deepest interest to re- 



THE ASTEROIDS. 129 

discover this stranger after its emergence from the sun's 
rays, a task of no little difficulty, as we will see by the 
slightest reflection. The star had been followed through 
only about 4° of its orbit, and on this slender basis it 
seemed almost impossible to erect a superstructure such 
as might conduct the astronomer to the point occupied at 
any given time by this almost invisible world. We shall 
see hereafter that this most astonishing feat was success- 
fully accomplished by the German mathematician and 
astronomer, Gauss, then quite a young man, and who, in 
this early effort, gave evidence of that high ability for 
which he became afterward so greatly distinguished. 

Ceres being re-discovered, and closely observed, the 
data were soon obtained for the exact computation of the 
elements of its orbit, when it was found to occupy, in 
the planetary system, the precise position which had been 
assigned to it fifteen years before by Baron de Zach, in 
accordance with the indications of the curious empirical 
rule, already presented, known as Bode's law. 

The harmony of the system was thus fully established, 
the missing term in the series was now filled. The vast 
interplanetary space between Mars and Jupiter was the 
real locality of a discovered world, whose existence had 
been conjectured by Kepler two hundred years before, 
and whose discovery, by combined systematic and scien- 
tific examination, constituted the crowning glory of the 
age. True, the new planet was exceedingly small when 
compared with any of the old planets, yet it acknowledged 
obedience to the great laws established by Kepler, re- 
volving in an elliptical orbit of very considerable eccen- 
tricity, and sweeping round the sun in a period of about 
four years and nine months, and at a mean distance 
of about 26 o millions of miles. 



130 THE ASTEROIDS. 

The telescope yielded but little information as to the 
absolute magnitude and condition of Ceres. Its diame- 
ter has been measured by various astronomers but the 
results are so discordant that but little confidence is to 
placed in them. It cannot, probably, exceed 1,000 miles, 
and may be much less. It is supposed to be surrounded 
by an extensive atmosphere, but the evidence of this is 
not very reliable. Under favorable circumstances, and 
with a powerful telescope, a disk can sometimes be seen, 
but for the most part Ceres presents the appearance of a 
star of about the eighth magnitude. 

Such was the condition of astronomy, affording to 
those interested cause for high gratification in the now 
known orderly distribution of the planetary orbs, when 
an announcement was made which was received with 
profound astonishment, as it at once introduced con- 
fusion precisely at the point in which order had been so 
lately restored. This was the discovery of another small 
planet, by Olbers of Bremen, revolving in an orbit nearly 
equal to that occupied by Ceres. Computation and 
observation united in fixing, beyond doubt, this most 
extraordinary discovery, and the new and anomalous 
body received the name of Pallas. The exact elements 
of the orbit of Pallas having been determined, it was 
found that a very near approximation to equality existed 
between the mean distances and periods of Ceres and 
Pallas, as we find below 



Ceres' period of revolution, 
Pallas' " " . 

Ceres' mean distance, . 
Pallas' " " 



1,682.125 days. 
1,686.510 " 
262,960,000 miles. 
263,435,000 " 



Here we find the mean distances and periods so nearly 
equal, that in case the planes of the orbits of the two 



THE ASTEROIDS. 131 

planets had chanced to coincide, these two worlds might 
travel side by side for a long while, and at a distance 
from each other only about double the distance separating 
the earth from her satellite. The distance between Mars 
and Ceres is no less than 120 millions of miles. The 
distance from Ceres orbit to that of Jupiter is more 
than 280 millions of miles, and yet here are two planets 
which may approach each other to within a distance less 
than half a million of miles. 

It is true, the eccentricities of the orbits differ greatly, 
and the inclinations of their orbital planes is also very 
great, so that Pallas, by this inclination, is carried far 
beyond the limits within which the planetary excursions 
north and south of the ecliptic had been previously con- 
fined, yet a time would come in the countless revolutions 
of these remarkable worlds when each would fill, at the 
same time, points of the common line of intersection of 
their orbital planes, and these two points, owing to the 
revolutions of the perihelion, might, possibly, at some 
future period, come to coincide. 

In case these speculations were within the limits of the 
probable, and if it were permitted to anticipate in the 
future, the possible collision or union of these minute 
planets, a like train of reasoning, running back into the 
past, would lead to the conclusion that in case their rev- 
olution had been in progress for unnumbered ages, there 
was a time in the past when these two independent worlds 
might have occupied the same point in space, and hence 
the thought that possibly they were fragments of some 
great planet, which, by the power of some tremendous 
internal convulsion, had been burst into many separate 
fragments. This strange hypothesis was first propounded 
by Dr. Gibers, and has met with more or less favor from 



132 THE ASTEROIDS. 

succeeding astronomers, even up to the present day, as 
we shall see hereafter. 

True or false, it soon produced very positive results, 
for it occasioned a renewal of the research which had been 
discontinued after the discovery of Ceres, and in a few 
years two more planets were added to the list of asteroids. 
The search was long continued, and it was not until the 
end of fifteen years that Olbers and his associates became 
satisfied that no more discoveries could be expected to 
reward their diligence. Thus it became a received doc- 
trine that in case a large planet had been rent asunder 
by some internal explosive power, it had been burst into 
four pieces, and that no other fragments existed sufficiently 
large to be detected even by telescopic power. 

This opinion prevailed up to December, 1845, when 
the astronomical world was somewhat startled by the 
announcement of a new asteroid, discovered by Henke, 
of Dreisen. This event awakened attention to this sub- 
ject, and a new generation of observers entered the field 
of research, whose efforts have resulted in revealing a 
large group of small planets, of which no less than fifty- 
five have already been discovered, and their orbits com- 
puted. 

The theory of the disruption of one great planet as 
the origin of the asteroids has been revived and exten- 
sively discussed, but thus far no satisfactory conclusion 
has been reached. So strangely are the orbits of these 
bodies related to each other that, in case they all laid on 
the same plane, they would in some instances intersect 
each other, exhibiting relations nowhere else found in the 
solar system. None of the asteroids are visible to the naked 
eye, nor are they distinguishable from the stars with the 
telescope, except under the most favorable circumstances. 



THE ASTEROIDS. 133 

When carefully watched some of them exhibit rapid 
changes in the intensity of their light, sometimes sud- 
denly increasing in brightness, and again as rapidly fad- 
ing out. These changes have been accounted for on the 
supposition that these worlds are indeed angular frag- 
ments, and that, rotating on an axis, they sometimes 
present large reflective surfaces, and again angular 
points, from whence but a small amount of light reaches 
the earth. 

As the stars of the smaller magnitudes are becoming 
more extensively and accurately charted, their places 
being determined with great precision, we may antici- 
pate a large increase in the number of known asteroids 
during the remainder of the current century, and so 
forward ; for if so great a multitude has already been re- 
vealed almost without effort, and nearly by accident, 
what must be the result when a systematic scheme of 
examination shall have been executed, based on an ac- 
curate knowledge of the places of all the stars down to 
the twelfth magnitude ? We have just ground for sup- 
posing that there are thousands of these little worlds 
revolving in space. 



CHAPTER VII. 

JUPITER, ATTENDED BY FOUR MOONS, THE SIXTH PLANET 

IN THE ORDER OF DISTANCE FROM THE SUN. 



Abo of Retrogradation»— Stationary Point. — Distance of the Planet De- 
termined. — Periodic Time. — Synodioal Eevolution gives the Sidereal, 
— Surface of Jupiter as given by the Telescope. — Period of Rotation. 
Diameter. — Volume. — Mean Distance. — Amount of Light and Heat. — ■ 
Figure of Jupiter. — Equatorial and Polar Diameters. — Discovery of 
the Four Moons by Galileo. — Effect on the Copeenican Theory. — 
Jupiter's Nocturnal Heavens. 

THE SATELLITES OF JUPITER.— How Discovered.— Their Magnitude.— 
Form of their Orbits. — Period of Revolution. — Eclipses. — Transits. — 
Occultations.— Telocity of Light Discovered.— Terrestrial Longi- 
tude. — Rotation of these Moons on an Axis. 



In passing from the diminutive asteroids to the mag- 
nitude and splendor which distinguish the vast orb which 
holds the next position in the planetary system, we are 
the more disposed to adopt the theory that the exceed- 
ing disparity now existing in the magnitude of these 
neighboring worlds is due to the fact that the asteroids 
are but a few of the fragments of some object in which 
they were all once united. We shall hereafter present 
a speculation on this subject which seems entitled to 
consideration. 

The planet Jupiter is one of the five revolving worlds 
discovered in the primitive ages. Its revolution among 
the fixed stars is slow and majestic, comporting well with 
its vast dimensions, and the dignity conferred by four 
tributary worlds. 



JUPITER. 135 

Like all the old planets, the ancients had determined 
with considerable precision the period of revolution of 
Jupiter, and his relative position among the planetary 
worlds. The points in his orbit where he becomes sta- 
tionary, the arc over which he retrogrades, and his period 
of retrogradation, were all pretty well determined from 
the early observations. 

As we recede to greater distances from the sun, the 
arc of retrogradation diminishes in extent, while the time 
employed in describing these arcs must by necessity in- 
crease. This will become evident if we recall to mind 
the cause of this apparent retrogradation. When the 
sun, earth, and planet, are all on the same straight line, 
the earth and planet being on the same side of the sun, 
then the planet is exactly in opposition. The earth and 
planet starting from this line, as the earth moves the 
swifter in its orbit, at the end of, say, twenty-four hours, 
the line joining the earth and planet will take a direction 
such that it will meet the first line exterior to the orbit 
of the planet, as seen below : — 




E P is the line on which the three bodies are found 
on the day of opposition. At the end of, say, twenty- 
four hours, the earth arrives at E in its orbit, the planet 
at P', and then the planet is seen From the earth in the 



136 



JUPITER 



direction E' P' S', whereas on the day previous it was 
seen in the direction EPS. Thus it appears to have 
moved backwards from S to S' among the fixed stars, 
while in reality it has moved forward in its orbit from P 
to P'. Admitting the orbits to be circles and the mo- 
tions to be uniform, it is very easy to locate the places of 
the earth and planet on successive days after opposition, 
and joining those places by straight lines, we should soon 
reach a position in which the lines thus drawn on con- 
secutive days would be parallel. There the planet would 
appear stationary among the fixed stars, and there its 
advance would commence, as is manifest from the figure 
below : — 




in which S is the sun, E E' E" E'" the successive places 
of the earth, P P' P" P'" the successive places of the 
planet. The lines E P and E' P' meet on the side op- 
posite the sun, the lines E' P' and E" P" also meet on 
the same side, but E /;/ P'" and E" P" are parallels, and 
in P" the planet becomes stationary, and after passing 
this point, the earth still advancing, the lines joining the 
earth and planet meet on the side next the earth, and 
henceforward the motion of the planet, as seen from the 



J UPITE R, 



137 



earth, must continue to be direct, until the earth coming 
round again to occupy the conjunction line, previous to 
which the stationary point will be passed, and the retro- 
gradation will be commenced. 

The distance of any planet from the sun, in terms of 
the earth's distance, may be obtained from a measure- 
ment of the arc of retrogradation in a given time, say 
twenty-four hours, provided we know the periodic time 
in which the earth and planet revolve round the sun 
This will become evident from the figure below — 




in which S is the sun, E and P the places of the earth 
and planet on the day of opposition, E' and P' their 
places at the end of twenty-four hours. E E' and P P' 
may be regarded as straight lines, as they are very short 
in comparison with the entire circumference. As we are 
supposed to know the periods of revolution of the earth 
and planet, the distances, E' E and P P, are fractional 
parts of the whole circumference, represented by one, di- 
vided by the number of days in the periodic time. The 
fraction for the earth is aei^, and for Jupiter it 



is 



4 3 3 2 . 5 8 * 

In the right-angled triangle, E'EO, we know the 



138 JUPITER. 

value of E' E, and the angle, E' E, equal to S'O S'J 
or the retrogradation of the planet. Hence the other 
parts become known either by construction or the 
simplest processes of trigonometry. We thus determine 
the value of E 0, and adding S E, we have the value 
of S 0. Then in the triangle S P' 0, we have the 
side S 0, just determined, also the angles P'S and 
P'OS. Hence we can construct the triangle, or com- 
pute by trigonometry the other parts. Thus S P', the 
planet's distance, becomes known. 

In case the periodic times were accurately known, and 
the orbits were exact circles, this mode of determining 
the distance of a superior planet would be sufficiently 
exact, but by the third of Kepler's laws, which tells us 
that the squares of the periodic times are proportional to 
the cubes of the mean distances, we perceive that the en- 
tire problem of the planetary distances resolves itself 
into fixing, with all possible precision, from observation, 
the periods of revolution, and then in obtaining the exact 
distance of any one of them. 

We have already stated that the interval elapsing from 
the passage of a planet from one side of the ecliptic to 
the other, up to the same again, gives the period of rev- 
olution, in case we correct for the various changes which 
may take place from one node-passage to the next. This, 
however, in the case of a planet like Jupiter, whose 
orbital plane nearly coincides with the ecliptic, becomes 
difficult as a matter of observation, and hence some better 
method must be employed. This is best accomplished 
by observing the exact time of opposition, or the moment 
when the planet is 180° distant from the sun. 

The interval between two such oppositions is called 
a synodical revolution, and in case the earth did not 



JUPITER. 139 

move, would be the planet's period of revolution around 
the sun. These synodical revolutions would be all pre- 
cisely equal on the hypothesis of circular orbits and 
equable motions. But as the planetary orbits are ellip- 
tical, and hence the motions variable, the synodical revo- 
lutions of any planet, as Jupiter, will vary somewhat 
from each other in duration. If, however, a large num- 
ber be counted, say, as many as have occurred in a thou- 
sand, or even two thousand years, then a mean period is 
deduced of great accuracy. 

This is possible, as we have the oppositions of the old 
planets, recorded by the ancients with sufficient precision 
to be employed in such a discussion. 

To derive the sidereal revolution from the synodical 
we have only to consider that the two bodies set out from 
the same right line. The earth's velocity is known ; the 
time required for the earth to overtake the planet is 
known (the synodical revolution). The velocity or rate 
of the planet's motion is required. This is readily found 
by simple proportion. Take the following example. In 
a mean solar day the earth travels in its orbit 0°.9856. 
A mean synodical revolution of Jupiter is observed to be 
equal to 398. 8G7 solar days. But the earth performs 
its revolution, and comes again to the starting point in 
365.256 days, and then must travel for 398.867 — 
365.256 = 33.611 days before overtaking Jupiter. But 
in 33.611 days, at the rate of 0°.9856 per diem, the 
earth will travel about 33°. 928, and this is the whole 
distance made by Jupiter in 398.867 days. Hence, his 
rate per diem is, ^^=4' 99=4' 59".2, and at this 

rate to travel 360 Q will require ™~ =4.382d, 14h. 

4 59 .2. 



140 JUPITER. 

2m., which is the time occupied by Jupiter in performing 
his revolution around the sun. 

These methods of investigation, which are perfectly 
simple, were employed by the ancients, and used even by 
Copernicus, Kepler, and others, and furnished the ap- 
proximate values of the periods and distances employed 
in the researches of Kepler, whereby he discovered his 
celebrated laws. 

Physical constitution of jupiter. — When examined 
with powerful telescopes the surface of Jupiter is found to 
be diversified with shades of greater or less depth, forming 
parallel bands or belts, especially about the equator of the 
planet. 

Upon these belts well-defined breaks, irregularities, 
and spots are discerned, by means of which it is dis- 
covered that the face of Jupiter, visible at any given time, 
is completely hidden by rotation on an axis, a new face 
appearing at the end of a little less than Jive hours. 
This gives a period of axical rotation of 9h. 55m. 49.7s., 
as the result of investigations similar to those employed 
in determining the period of rotation of Mars. 

When the apparent diameter of Jupiter is accurately 
measured, and his distance is taken into consideration, 
we find his actual diameter to be nearly 90,000 miles , 
and his volume to be equal to that of 1,281 globes such 
as our earth. 

The dark belts which encircle the equatorial regions of 
the planet, and which revolve with the globe, show that 
the axis of rotation is very nearly perpendicular to the 
plane of the orbit. 

Thus we have a planet twelve hundred and eighty- 
one times larger than our earth, rotating on an axis, but 
little inclined to the plane of its orbit, in less than ten hours 



JUPITER 




ALLA VISTA.TENERIFFE 1856 



JUPITER. 141 

of time, and sweeping round the sun in about twelve of our 
years, at a mean distance of about 485 millions of miles. 

The streaks and dark shades which distinguish the 
equatorial region of Jupiter are by many considered to 
be belts of clouds floating in the atmosphere of the 
planet, thus indicating the existence of all the great ele- 
ments which distinguish the earth. In consequence of 
the fact that the axis of Jupiter is very nearly perpen- 
dicular to the plane of the orbit, the sun will always 
pour his rays vertically on the equator of the planet, 
constituting one perpetual summer in all parts of the 
globe. In case light and heat are governed by the same 
laws which hold on the earth, the inhabitants of Jupiter 
will receive from the sun only one twenty-seventh part 
as much light and heat as falls on the earth. What mo- 
difications of heat may be effected by the extensive atmos- 
phere which appears to surround Jupiter it is impos- 
sible to conjecture. We may suppose, without reflection, 
that a world would be only dimly illumined whose sun 
was reduced to one twenty-seventh part of that which 
lights our earth. This, however, is not the case, as any 
one will credit who has ever witnessed the flood of light 
poured forth from the smallest portion of the sun's disk 
in emerging from total eclipse. The amount of light 
which falls on Jupiter far exceeds that which is poured 
upon the earth on a moderately cloudy day. 

When we measure rigorously with the micrometer the 
figure of Jupiter's disk, we find a marked deviation from 
the circular outline. This is analogous to the figures of 
the earth and Mars, and indeed the same peculiarity (of 
which a satisfactory account will be given hereafter) dis- 
tinguishes all the planets. In Jupiter the equatorial diam- 
eter exceeds the polar by more than six thousand miles. 



142 JUPITER. 

We are indebted to the telescope for the revelation of 
the highly interesting fact that Jupiter is attended by no 
less than four moons or satellites, nearly all of them 
larger than our own moon. These satellites were dis- 
covered by Galileo in 1610, soon after he had finished 
his second telescope, which, as he tells us, cost him in- 
credible pains, and which bore a magnifying power of 
about thirty times. The discovery of these moons of 
Jupiter may be regarded as among the most important 
results of the application of the telescope, if we take into 
account the then existing condition of astronomical 
science. The scientific world was just in a transition 
state. The most honest, intelligent, and powerful minds 
had already adopted the Copernican theory, but in the 
universities and other schools of science, as well as in the 
church, the system of Ptolemy still reckoned among its 
supporters a host of learned and dignified men. The 
beautiful miniature of the solar system presented in 
Jupiter and his moons, as given by Copernicus, could 
not fail to exert a most powerful influence over all candid 
and unprejudiced minds. Here was presented to the eye 
a central orb and about it a scheme of dependent worlds 
revolving in circular orbits, and with such elegant sim- 
plicity as to shame the cumbrous complexity which dis- 
tinguished the epicyclical theory of the old Greek school. 
It is not at all surprising that Galileo, the discoverer of 
this beautiful system, should have become one of the 
most ardent supporters of the doctrines of Copernicus. 

These satellites of Jupiter revolve in orbits whose 
planes are nearly coincident with the equator of their 
primary. The exterior, or most distant of the four, 
revolves in an orbit somewhat inclined to the plane of 
Jupiter's equator, but the three inner satellites, at every 



JUPITER. 143 



revolution, eclipse the sun to the inhabitants of Jupiter, 
and are themselves eclipsed in passing through the shadow 
of their primary. The same phases which mark the 
revolution of our moon are also exhibited by Jupiter's 
moons, and the periods of revolution of three of the satel- 
lites are so adjusted that one of them must be full when 
the other two are new. 

The nocturnal heavens, as seen from this grand orb, 
must be inexpressibly magnificent. Besides the same 
glittering constellations which are seen from earth, the 
sky of Jupiter may be adorned with no less than four 
moons, with their diverse phases, some waxing or waning, 
some just rising or setting, some possibly just entering 
into or emerging from eclipse. 

The whole of this splendid celestial exhibition, sweep- 
ing across the heavens, rising, culminating, and setting, 
in less than five hours of our time. Such are the scenes 
witnessed by the inhabitants of Jupiter, if such there be. 

The sattelites of jupiter. — As already stated, 
these tributary worlds were discovered by Galileo in 
1610. On the evening of January the 8th, of that year, 
having completed his second telescope, capable of bearing 
a magnifying power of thirty times, he went to his garden 
to test its quality by an examination of Jupiter. Near 
the planet he noticed three small stars, nearly in a straight 
line, passing through the center of Jupiter. He sup- 
posed them to be fixed stars, but carefully noted their 
positions with reference to Jupiter and to each other. 
On the following night, he remarked that there was a 
manifest change in the relative places of these stars and 
the planet which could hardly be accounted fur by the 
motion of Jupiter in his orbit. 

Galileo began to suspect the true nature of the stars 



144 JUPITER. 

which had attracted his attention, and seeing clearly the 
immense importance of such a discovery, awaited with 
great impatience the coming of the next evening to con- 
firm his conjectures. Clouds, however, coming up dis- 
appointed his hopes, and it was not until the evening of 
the 14th that he was again permitted to direct his tele- 
scope to the planet, when he found, to his great delight, 
not only the three stars, still in close proximity to the 
planet, but he also detected a fourth one, whose appear- 
ance and position were such that he announced at once 
the discovery of four moons resembling our own, and re- 
volving about the planet Jupiter as their central orb. 

This announcement created the greatest excitement in 
the astronomical world. Its effect on the old theory of 
astronomy was at once perceived, and the disciples of 
Ptolemy determined that they would never believe in the 
existence of any such pestilent worlds. Some of them 
actually refused to do so much as look through the tube 
of Galileo, declaring the whole was a deception, and un- 
worthy the attention of a true philosopher. 

The discovery was not the less real because its truth 
was denied, and to this important addition to the bodies 
which constitute our system modern science is indebted 
for some of its most elegant discoveries. 

The great distance at which we are compelled to exam- 
ine these bodies has rendered it difficult to obtain, even 
with our most delicate instruments, satisfactory measures 
of the diameters of these satellites. Approximate meas- 
ures have been obtained from which we learn that the 
nearest satellite has a diameter of about 2,500 miles, the 
second, 2,068; the third, 2,377; the fourth, 2,800 
miles. We name them in the order of their distances 
from the primary. 



JUPITER. 145 

By careful measures of the elongations, or greatest 
distances to which these bodies recede from their primary, 
the magnitude and form of their orbits have been well 
determined. The first satellite is thus found to revolve 
round Jupiter in an orbit nearly circular, whose diameter 
is 260,000 miles, in a period of Id. 18h. 28m. The 
plane on which the orbit lies is inclined to the plane of 
Jupiter's orbit, under an angle of 3° 05' 30", or less, by 
nearly one-half, than the angle made by the moon's orbit 
with that of the earth. The smallness of this angle, 
the nearness of the satellite to its primary, the immense 
magnitude of the primary and the distance from the sun, 
combine to produce an eclipse of the first satellite at 
every revolution, while, in like manner, an eclipse of 
the sun takes place quite as frequently, from the fact that 
the shadow of the satellite falls on the planet at every 
conjunction of the satellite with the sun. These state- 
ments are not mere conjectures. They are verified by 
the telescope, for these eclipses of the satellite and the 
shadows cast on the primary arc distinctly seen from the 
earth, and furnish the data whereby the periods of revo- 
lution are determined with great precision. When Jupi- 
ter is in opposition it often occurs that the satellite when 
on the hither side of the primary, is seen projected on tho 
disk of the planet as a round bright spot, while the 
shadow of the same body may be seen in close proximity 
as a round black spot. Any eye, situated within the 
limits of this shadow, will witness an eclipse of the sun 
precisely such as is produced on earth by the shadow of 
tho moon. The passage of the satellite across the disk 
of Jupiter is called a transit. From this position the 
moon of Jupiter revolves round half its orbit, and then by 
necessity passes across the cone of shadow east by tho 



146 



JUPITER 



primary in a direction opposite the sun. Here we be- 
hold an eclipse of the secondary, as its light is extin- 
guished on entering the shadow, and is only regained 
after passing beyond the limits of the shadow, thus de- 
monstrating beyond a doubt the fact that, like our moon, 
these secondaries of Jupiter shine only by reflecting the 
light of the sun. 

In case Jupiter were at rest, it is evident that the ob- 
servations of these eclipses would give the exact period 
of revolution of the satellite, which would be precisely 
the interval from one eclipse to the next. The fact that 
the earth is in motion would not affect the time of recur- 
rence of the eclipse, for this would be entirely independ- 
ent of the place of the spectator, provided he sees the 
disappearance of the satellite at the moment its light is 
extinguished. It is manifest that the motion of Jupiter 
in his orbit will change the position of the axis of the 
shadow, and as the satellite revolves in the same direc- 
tion in which the shadow advances, it is clear that the 
time from one eclipse to the next is longer than the true 
period of revolution of the satellite, by a quantity easily 
computed from the known orbital velocity of the planet, 
as may be seen from the figure below, where — 




JUPITER. 147 

S is the sun's place, E, the earth, J, Jupiter in opposi- 
tion, M, the satellite in eclipse. At the end of one 
exact revolution of the satellite, Jupiter has reached J', 
the satellite is at M', but the axis of shadow is now J' M", 
and the center of the eclipse will not occur until the 
satellite reaches M", passing over the angle M" J' M'. 
This angle is precisely equal to the angular motion from 
eclipse to eclipse, a quantity easily determined. The 
satellite will then revolve 360°, -f the angle J S J', or 
M' J ; M", in the interval from one eclipse to the next, 
hence the rate per hour becomes known, and gives at once 
the period of revolution. 

Galileo devoted himself for many years to a careful 
observation of the eclipses of Jupiter's moons, and finally 
constructed tables whereby these eclipses might be pre- 
dicted with tolerable precision. His successors devoted 
much time to the same subject, for a reason we will give 
hereafter. Long study of these phenomena revealed the 
curious fact that the interval from one eclipse to the next 
did not fulfil the prediction based on the foregoing reason- 
ing. The place of the earth seemed in some mysterious 
way connected with the time at which the eclipse occur- 
red. This may to some appear very reasonable, but, in 
fact, on the hypothesis that at the moment of the extinc- 
tion of a luminous object it ceases to be visible, the place 
of the earth in its orbit or the position of the observer 
could in no way affect the moment of the satellite's dis- 
appearance by entering the shadow of its primary. This 
will become manifest from a very simple illustration. 
Suppose the persons in a large circular hall to be gazing 
on the light of a taper, and the taper is suddenly extin- 
guished by being blown out, every observer will certainly 
loso the light at the same absolute moment, admitting 



148 JUPITER. 

the fact that the light dies at the instant of extinction to 
every eye. Let us apply this illustration to the eclipses 
of Jupiter's moons. They are only seen when the sun- 
light falls on them. Cut off from them the sunlight by 
entering the shadow of the primary, and admitting this 
entrance to be instantaneous, every eye everywhere should 
lose the light at the same moment of absolute time. 

The earth's position in its orbit ought, therefore, to 
have no effect on the time of the eclipse, and yet it be- 
came clearly manifest that the earth's place was in some 
way connected with certain irregularities in the intervals 
of these remote eclipses. This matter will be best illus- 
trated from the figure below, in which S represents 




the sun, E E' E" E r// the earth's orbit, J Jupiter, 
and S the satellite. It was found that when the 
earth was at E, or nearest to Jupiter, the interval from 
eclipse to eclipse grew longer as the earth receded from 
Jupiter. At E' the interval was at a maximum. It 
now diminished by slow degrees, becoming nearly station- 
ary at E", then growing shorter, reached a minimum at 
E'", after which a slow increase was noticed up to E, 
and so on in every revolution of the earth in its orbit. 
Due account, of course, must be taken of the orbital 



JUPITER. 149 

movement of Jupiter. In case the student is ignorant of 
the explanation of these variations in the synodical revo- 
lutions of the moons of Jupiter, he may test his own 
powers of discovery by a close examination of the facts 
as above presented. All the satellites gave evidence of 
the same facts, and the irregularities were found to follow 
in the same order, reaching their maxima, minima, and 
stationary points at the same time, or when the earth 
was at the same point of its orbit. 

More than fifty years passed away without any satis- 
factory explanation of the facts and phenomena above re- 
corded, when, in 1675, Roemer was at length successful 
in solving the mystery, and found it due to the progress- 
ive motion of light, which up to this time had been con- 
sidered by all philosophers as instantaneous in its effects ; 
that is, if a luminous body were created, all eyes, no 
matter how remotely placed, would see the light at the 
same moment of time. As the velocity of light, deduced 
from these investigations, is so enormous, no less than 
192,000 miles in one second, we will enter into the 
explanation somewhat minutely. Suppose a luminous 
body, as in the figure below, at S, suddenly to be ex- 
tinguished, the stream of light flowing from the body is 

^ A B 

S 

at once cut of, and when tho last particles or wave passes 
a spectator at A, at that moment he will mark the ex- 
tinction of the light, while to the spectator at B tho 
really extinct luminous body will remain visible until the 
last particles of the stream of its light pass B, and then 
the body vanishes to the spectator at ]>. Suppose the 
body to thus disappear periodically, A and B will, while 



150 JUPITER. 

they remain stationary, note the intervals from one dis- 
appearance to the next to be precisely equal, and the in- 
terval, as observed by A, though beginning at an earlier 
absolute moment of time, will be equal to the interval, 
as observed at B. Let us now suppose, that after a dis- 
appearance, and before the next, A removes to B, it is 
manifest that the duration or period whose beginning was 
observed at A, but whose ending was noted at B, will be 
longer than it was before by an amount of time required 
for the stream of light to pass from A to B. The reverse 
would be true if B changed his position to A. 

These principles are precisely applicable to -the case 
under consideration. If the earth's orbit were a straight 
line, with a length equal to A B, the conditions would be 
identical. The nearly circular figure of the earth's orbit 
produces the variations already noticed. When the earth 
is rapidly receding from the source of light, the dura- 
tion of the synodical revolution of Jupiter's moon will be 
increased by the time required for the light to pass over 
the space traversed by the earth during the synodic rev- 
olution. This period amounts to some seventeen days 
for the fourth satellite. But the earth travels some 
68,000 miles an hour, or in seventeen days nearly thirty 
millions of miles, so that the synodical revolution, when 
longest, will exceed the same period when shortest by an 
amount equal to the double time required by light to 
travel 30,000,000 of miles. This difference between the 
maximum and minimum synodic periods, proved to be 
about five minutes, and hence it became evident that 
light must fly at the rate of sixty millions of miles in five 
minutes or 12,000,000 miles in one minute or 192,000 
miles per second. 

Should this result appear incredible we shall find 



JUPITER. 151 

hereafter abundant confirmation of its truth by a train 
of reasoning and phenomena entirely distinct from what 
have just been given. 

In case light travels with a finite velocity we cannot 
fail to perceive that this fact will introduce important 
modifications in all observations designed to fix the places 
of the heavenly bodies at a given moment of time. Since 
the earth is sweeping through space with great velocity 
even this fact will produce a certain displacement in the 
apparent place of a fixed luminous body. When the 
body under observation is in motion, the velocity of light 
being finite, it is clear that the light which falls on the 
eye of the spectator, and which enables him to see the 
object, is not the light emitted at the moment the object 
is seen. Thus, the planet Jupiter is distant from the 
earth, say, 480 millions of miles. To travel this distance 
his light must occupy no less than forty minutes, during 
which time Jupiter has advanced in his orbit about one- 
third of his own diameter. During the same time the 
earth has traveled in its orbit a certain distance nearer to 
or further from Jupiter, which must be taken into account 
in our effort to fix the absolute position of the planet's 
center at a given moment. This subject will be resumed 
when we come to consider the means and instruments em- 
ployed in astronomical observation. 

The satellites of Jupiter have furnished, in their eclipses, 
the earliest method of resolving the great problem of 

Terrestrial longitude. — The position of any place 
on the earth's surface is determined by fixing its distance 
from the equator of the earth, north or south, called the 
latitude, and also its distance east or west of any given 
meridian line, called the longitude. The first of these 
elements is very readily determined. In ease a place is 



152 JUPITER. 

situated on the equator, its latitude is zero, and to any 
spectator at this place, as we have already shown, the 
poles of the earth and heavens will lie on the horizon. 
Leaving the equator and traveling due north along a 
meridian line, for every degree we go north it is evident 
the pole of the heavens will rise one degree above the 
horizon ; and when we reach the north pole of the earth, 
the north pole of the heavens will be on the zenith, or 
ninety degrees above the horizon. 

Thus it appears that the latitude of any place is equal 
to the elevation of the pole above the horizon of the 
place, and to fix the latitude we have only to measure this 
angle of elevation with a suitable instrument, and apply 
certain corrections, to be hereafter explained. The pro- 
blem of the longitude does not admit of so easy a solu- 
tion. To determine accurately longitude at sea is a mat- 
ter of the highest importance to commerce and navigation, 
a problem for whose solution maritime nations have in 
modern times offered large rewards. The safety of a 
vessel, its crew and cargo, depends on learning by some 
method its exact position on the surface of the ocean, 
where there are no permanent objects on our globe to 
mark its place ; and it is only from the celestial sphere 
that it becomes possible to select fixed objects which may 
reveal to the mariner the dangers by which he is sur- 
rounded. 

The latitude, as we have seen, is readily obtained; 
not so the longitude, which had, up to time of Galileo, 
been regarded as almost an impossible problem at sea. 
The great Florentine astronomer saw in the eclipses of 
the moons of Jupiter the means of solving this highly 
important problem, and to this end he devoted many 
years to most diligent and careful observation of these 



JUPITER. 153 

eclipses, with a view to be able to predict their coming, 
months or even years in advance. We will now explain 
how these predicted eclipses of Jupiter's satellites, con- 
joined with their actual observation, may be employed 
in the determination of terrestrial longitude. 

As the earth rotates on its axis with uniform velocity, 
the 360 degrees of the earth's equator are fairly repre- 
sented by twenty-four hours of time. Thus an hour of 
time is equal to 15° of longitude, a minute of time is 
equal to 4' of longitude, a second of time is equal to 4" 
of longitude. The difference of longitude, then, of any 
two places on the earth's surface is nothing more than 
the difference of local time, for a mean time solar clock 
marks Oh. 00m. 00s. when the center of an imaginary 
sun, moving with the mean or average velocity of the 
true sun, reaches the meridian of the place in question. 
A place west of the first one will have the center of the 
mean sun on its meridian later by an amount of time 
equal to the exact difference of longitude. It is clear, 
then, that if any phenomenon, such as the sudden extinc- 
tion of a fixed star, could be noted by two observers in 
different places, each will record the moment of disap- 
pearance in his own local time, and an inter-comparison 
of these records will give at once the difference of longi- 
tude between the two stations. 

Suppose it were possible to predict that the bright 
star Vega, in the constellation of the Lyre, would sud- 
denly disappear on the first day of January, 1870, at 
Oh. 00m. 00s. mean time at Greenwich, England, this 
fact being known and published', vessels at sea on long 
voyages, in all parts of the globe, having the star above 
their horizon, by watching for this phenomenon, and by 
noting the moment of disappearance in their local time, 



154 JUPITER. 

would determine their longitude from Greenwich. All 
observers recording the disappearance before the pre- 
dicted time would be in east longitude, while those re- 
cording the same phenomenon later than the predicted 
time would be in west longitude, and as many hours, 
minutes and seconds west as was indicated by their local 
time. 

Now, at sea, very simple methods, as we shall show 
hereafter, may be employed to obtain the local time, and 
thus, were it possible to predict a multitude of such phen- 
omena as above recorded occurring every day or two, 
for years in advance, seamen on long voyages, providing 
themselves with these predictions, would have the means 
of fixing their longitude as often as any one of those pre- 
dicted phenomena could be observed. 

The eclipses of the moons of Jupiter are precisely like 
the phenomenon of the sudden extinction of a star. As 
these moons shine only by reflected light, the moment 
they enter the shadow of their primary they vanish from 
the sight, or are, to all intents and purposes, extin- 
guished ; and as these eclipses are constantly recurring 
at very short intervals,* Galileo saw at once the use to 
which they might be devoted in the resolution of this 
great problem of terrestrial longitude. 

Before they could be thus used it became necessary 
to master completely their laws, so that the moment of 
eclipse might be accurately predicted years in advance. 
Though the Tuscan philosopher did not live long enough 
to perfect and apply his great discovery, his successors in 
modern times have fully carried out and applied what 
was so admirably conceived and so carefully com- 
menced. 

An attentive examination of the luminosity of Jupi- 



JUPITER. 155 

ter's moons reveals the curious fact that it is variable, 
increasing and decreasing at regular intervals, equal to 
the periods of revolution in their orbits, whence it has 
been inferred by Sir William Herschel and others that 
each of these satellites rotates (like our moon) upon an 
axis in the exact time in which it revolves about the 
primary. 



CHAPTER VIII. 

SATURN, THE SEVENTH PLANET IN THE ORDER OF DIS- 



The most Distant of the Old Planets.— Its Light Faint, but Steady.— 
Synodical Revolution. — The Sidereal Revolution. — Advances in Tele- 
scopic Discovery.— Galileo announces Saturn to be Triple. — Huygenb 
Discovers the Eing. — Division of the King into Two. — Cassini an- 
nounces the Outer Eing the Brighter. — Multiple Division. — Shadow 
of the Planet on the Eing. — Belts and Spots.— Period of Eotatiox 
of the Planet and Eing.— Disappearance of the Eing Explained. — Thb 
Dusky Eing. 

SATELLITES OF SATUEN.— By whom Discovered— Eight in Number.— 
Their Distances and Periods.— Saturn's Orbit the Boundary of thb 
Planetary System, as known to the Ancients. 



We now reach, in our outward journey from the sun, 
the most distant world known to the ancients, revolving 
in an orbit of vast magnitude, and in a period nearly 
thirty times greater than that of our earth. Saturn, on 
account of his immense distance, shines with a fainter 
light than either of the old planets, though still a con- 
spicuous object among the fixed stars. Its light is re- 
markably steady, without the scintillations which dis- 
tinguish the stars, and the brilliant glare which is shown 
by Venus and Jupiter. There is a yellowish or golden 
hue to this planet which is not lost when seen through 
the most powerful telescopes. 

Such is the planet Saturn as known to the old astrono- 
mers, and as seen by the unaided vision. Its movement 



SATURN. 157 

among the fixed stars is distinguished by the same phen- 
omena which we have found to exist among all the plan- 
ets. Being the most remote of all the old satellites of 
the sun, its stations are the best defined, its arc of retro- 
gradation the shortest, and the period employed in this 
retrograde movement is longest. From observations 
made during opposition, and by trains of reasoning iden- 
tical with those laid down in our examination of Jupi- 
ter, the periodic time and mean distance of Saturn are 
concluded. . 

Owing to the very slow motion of this planet in its 
orbit, the earth will pass between it and the sun, or bring 
it into opposition, in a little over 378 days ; that is, Saturn 
and the earth starting from the same straight line, pass- 
ing through the sun, the earth makes its revolution, 
comes up to the starting point, and then overtakes 
Saturn in about twelve days and three-quarters. The 
earth's period must then be to that of Saturn as twelve 
days and three-quarters is to 378, or as one to thirty, 
roughly. 

This determination is a matter of such simplicity that 
any one, almost without instruments, may make the ob- 
servations which give the data for the computation. The 
opposition is observed when Saturn is. 180° from the sun, 
and we have only to count the days from one opposition 
to the next to obtain the synodical revolution. 

Such were the few facts known to astronomy touching 
this distant orb prior to the discovery of the telescope. 
The immense multiplication and extension of- human 
vision effected by the invention and improvement of that 
instrument is in no ease more signally displayed than in 
the successive revelations which have been made in the 
physical constitution of Saturn, and the extraordinary 



158 SATURN. 

appendages and scheme of dependent worlds now known 
to revolve around him. 

In 1610, the year in which Galileo first applied the 
telescope to an examination of the celestial orbs — the 
year in which he announced the discovery of Jupiter's 
moons — an examination of Saturn resulted in the strange 
and anomalous discovery that his disk was not circular, 
like all the other planets, but elongated, as though two 
smaller planets overlaid a larger central one extending 
somewhat to the right and left of the center. This re- 
markable figure Galileo announced to his astronomical 
contemporaries under the form of a puzzle produced by 
a transposition of the Latin sentence — 

" Altissimum plane tarn tergenimum observavi." 

"I have observed the most distant of all the planets 
to be triple." 

This mode of presenting the discovery was adopted by 
the Florentine astronomer to establish his priority, as 
many of his great discoveries were claimed by some of 
his opponents, while the truth of all was most obstinately 
disputed by others. It was urged, even in the case of 
Jupiter's moons, that these were mere illusions, the off- 
spring of the heated imagination of the ambitious philoso- 
pher, and that other eyes could never verify these pre- 
tended discoveries. We can readily imagine what must 
have been the feelings of Galileo when, not many months 
after the discovery of the triple character of Saturn, he 
was compelled to acknowledge that, even as seen through 
his most powerful telescope, the planet was exactly cir- 
cular, with an outline as sharp and perfect as that of 
Jupiter. He exclaims, "Can it be possible some demon 
has mocked me!" He did not live to explain this re- 



SATURN. 159 

markable change, but he saw the triple form restored, 
and discovered these periodical transmutations of figure. 

Fifty years later, in 1659, Huygens, with more power- 
ful telescopes, discovered the true figure of Saturn, and 
found the triple form seen by Galileo to be produced 
by the fact that the round planet was encircled by a 
broad, flat ring of immense diameter, and so situated 
that the spectator on the earth can never see it in a 
direction perpendicular to its plane. Hence, although 
circular in form, the direction of the visual ray gives it 
an oval or elliptical figure. Huygens distinctly per 
ceived the dark space intervening between the body of the 
planet and the ring, right and left, which had escaped 
the eye of Galileo with a less perfect telescope. Hence, 
the Florentine astronomer only saw the planet elongated, 
and pronounced it triple. Huygens explained the mys- 
terious change of figure which had so perplexed Galileo, 
and found it due to the fact that the ring is extremely 
thin, so thin, indeed, that when the earth chances to hold 
a place such that the plane of the ring produced passes 
through the earth and the ring comes to be presented to 
the spectator edgewise, not even the telescope of Huygens 
could discern the fibre of light presented by the rim, or 
circumference of the ring, when thus located, and to them 
the disappearance was complete, leaving the planet round, 
clear, and well-defined. 

In 1665, what had hitherto been regarded as ono 
broad, flat ring, was observed to be divided into two por- 
tions by a dark line, which, under favorable circum- 
stances, was traced entirely round the ring. This dis- 
covery was confirmed by the elder Cassini, in 1675, who 
also discovered the unequal brilliancy of the two rings, 
the outer one being the brighter, lie also was the fust 



160 SATURN. 

to announce the existence of a dark stripe or belt sur- 
rounding the equator of the planet. Other discoveries, 
such as additional belts, the shadow of the planet on the 
ring, the shadow of the ring on the planet, were succes- 
sively made, as the powers of the telescope were improved. 
During the present century many astronomers assert the 
multiple division of the rings of Saturn, and the evidence 
is so conclusive, that the existence of dark lines, concentric 
with the rings, (and like that which severs the two prin- 
cipal rings, cannot be denied, ) though there is every rea- 
son to believe that these lines are only to be seen oc- 
casionally. With the full power of the refractor *of the 
Cincinnati Observatory, denning in the most beautiful 
manner all the other delicate characteristics of Saturn 
and his rings, I have never been able to perceive any 
trace of any other than the principal division. 

The bright and dark belts and certain spots, which 
mark both the surface of the planet and the ring, have 
furnished the means of fixing the period of rotation of 
the planet on its axis at lOh. 29m. 16.8s., while the ring 
revolves on an axis nearly coincident with that of the 
planet in lOh. 32m. 15s. 

If we reflect on the structure and position of Saturn's 
rings, the phenomena attending its disappearance and 
reappearance become readily explicable. The plane of 
the ring produced indefinitely, intersects the plane of the 
earth's orbit in a straight line. This is called the line 
of nodes of the ring. This line of nodes, remaining 
nearly parallel to itself, will manifestly move as the ring 
moves, carried with the planet in its revolution round the 
sun. During one-half of Saturn's revolution in its orbit 
the sun will illumine the northern side of the rings, 
during the other half it will shine on the southern side. 




SATURN, CINCINNATI OBS 



SATURN. 161 

Thus the ring, carried by the planet, will finally come 
into a position such that the sunlight will fall on neither 
side, but on the edge of the ring only, and when in this 
position it is manifest that the plane of the ring passes 
through the sun. If, when in this position, the earth 
comes between Saturn and the sun, a spectator from the 
earth's surface will behold the edge of the ring, if visible 
at all, as a delicate line of light extending beyond the 
disk of the planet, and passing through its center. 

The earth, moving forward in its orbit from opposi- 
tion of the planet, will pass through the plane of the 
ring, and upon the non-illuminated side. As Saturn 
moves very slowly in comparison with the earth, while 
the plane of the ring is sweeping from the one side of the 
sun to the other, the earth may pass more than once 
through the plane of the ring, repeating, in some sense, 
the phenomenon of disappearance. As Saturn's period 
of revolution extends to nearly thirty of our years, during 
one- half of this period the inhabitants of the earth will 
behold one side of the ring, and during the other half 
they will look upon its opposite surface. All the changes 
from the greatest opening of the ring, when the planet is 
seen like a magnificent golden ball, engirdled by its ring 
of golden light, down to the total disappearance of the 
ring, require about fifteen years. Then the reverse 
changes occur, and all the phases and transmutations are 
accomplished in about thirty years, when they are again 
repeated in the same order. 

The disappearance of the ring, which took place in 
1848, was watched by the author at the Cincinnati Ob- 
servatory with the powerful refractor of that institution. 
A minute fibre of light remained clearly visible even 
when the edge of the ring was turned directly to the 



162 SATURN. 

eye of the spectator. The delicacy of this line far ex- 
ceeds anything ever before witnessed. When compared 
with the finest spider's web stretched across the field of 
view, the latter appeared like a cable, so greatly did it 
surpass in magnitude the filament of light presented in 
the edge of Saturn's ring. I had the pleasure of witness- 
ing the phenomena so beautifully described by Sir Wil- 
liam Herschelj the movement of the satellites along this 
line of light, "like golden beads on a wire." This is a 
consequence of the coincidence of the planes of the orbits 
of these satellites with the plane of the ring ; hence, when 
the ring is seen edgeways, these orbits will, in like man- 
ner, be seen as straight lines, coincident with the line 
under which the ring is seen. 

To add to the extraordinary constitution of this wonder- 
ful planet, another ring has recently been discovered by 
Bond, of Cambridge, and by Lassell, of Liverpool, more 
mysterious, if possible, than those previously known. 
This ring lies between the planet and the bright ring, 
and is of a dusky hue, and only discernible in powerful 
telescopes. Its outline is the same as that of the other 
rings, with the inner edge of the smaller of which it 
seems to unite. This extraordinary appendage is so con- 
stituted as to reflect but little light, and is sufficiently 
translucent to permit the body of the planet to be seen 
through its substance. I have frequently examined this 
dusky ring with the Cincinnati refractor, and have some- 
times been confident that its breadth at the extremities of 
its longer axis was much greater than that which would 
be due to an elliptical figure concentric with the bright 
rings. 

Knowing, as we do, the distance of Saturn, it is easy, 
from the measures of the diameter of his surrounding 



SATURN. 163 

rings, to compute their absolute dimensions. The ex- 
terior diameter of the larger ring is no less than 176,418 
miles, and its breadth is 21,146 miles. The exterior 
diameter of the second ring is 157,690 miles, leaving a 
chasm between the bright rings of 1,791 miles across. 
The breadth of the second ring is 34,351 miles, and the 
interval between the planet and this ring is 19,090. 
miles. The thickness of the rings is a matter of con- 
jecture, as it is too minute a quantity to be obtained by 
any means of measurement at present within our reach. 
Sir John Herschell does not believe it can exceed 250 
miles. A single second of arc, at a distance equal to Sa- 
turn, subtends nearly 5,000 miles ; so that a bright globe 
of 5,000 miles in diameter, removed to Saturn's distance, 
would be covered by the smallest spider's web stretched 
across the field of view of the eye-piece of the telescope. 
In case we admit the rings of Saturn to be 250 miles in 
thickness, then, when seen edgeways, the filament of light 
seen reflected from the outer circumference is only one- 
twentieth part the diameter of the spider's web. 

We pass now to an examination of the 

Satellites of Saturn. — The largest of these satel- 
lites was discovered by Huygens as early as 1665. Four 
others were discovered some thirty years later by Cassini. 
Two more were added by Sir William Herschel on the 
completion and application of his grand reflector in 1789, 
while an eighth satellite was discovered by two observers, 
Bond and Lassell, on the same night (Sept. 19th, 1848), 
the one in Cambridge, United States, the other in Liver- 
pool, England. Wo have thus, in addition to the anom- 
alous rings which surround Saturn, a scheme of no 
less than e'vjht dependent worlds, all of which revolve 
about the central orb in elliptical curves, and in periods 



164 SATURN. 

varying from twenty-two hours to seventy-nine days. 
If the celestial scenery of Jupiter is rendered magnificent 
by the splendor of his four moons, what must be the 
amazing grandeur of the nocturnal sky of Saturn, arched 
from horizon to horizon by his broad, luminous girdle 
(on which the shadow of the planet, like the dark hand 
of a mighty dial, will mark the hours of the night), the 
changes, phases, eclipses, the occupations of his numer- 
ous moons, and the brilliant background of glittering 
constellations which gem our nocturnal sky, must alto- 
gether form a display of celestial splendor of which the 
human mind can form but a faint conception. 

In consequence of the vast distance at which the Sa- 
turnian system is removed, and the magnitude and power 
of the telescope demanded for its examination, we are 
as yet comparatively ignorant of many facts, which, in 
the case of Jupiter's moons, have been well determined. 
It will be remembered that the moon's distance from the 
earth is about 237,000 miles. Three of Saturn's moons 
fall far within this limit, and the fourth is but 243,000 
miles from its primary. The fifth is 340,000 miles dis- 
tant; the sixth, 788,000 miles; the seventh (latest dis- 
covered), is about 1,000,000 miles distant, while the 
eighth is removed from Saturn to a distance of nearly 
2,300,000 miles. 

The nearest of the moons, revolving at a distance of 
120,000 miles, circulates round the primary in about 
twenty-two hours and a half, presenting all the phases 
exhibited by our moon, in less than a thirtieth part of 
the time. Its disk, as seen from Saturn, will surpass 
the moon's disk in the ratio of ten to one. Of the five 
earliest discovered satellites, two are readily seen with 
any good telescope. The five may now be seen by many 



SATURN. 165 

refractors and reflectors of modern construction, while 
the three smallest satellites are only rendered visible by 
a few of the most powerful instruments in the world. 

We shall here close what we have to present of the 
structure of the Saturnian system. We have thus ter- 
minated the examination of all planetary bodies known 
to the ancients, and have added to these the new objects 
revealed by the telescope, inclosed by the circumscrib- 
ing orbit of Saturn. Within these limits we find all the 
phenomena known to the master minds to whom we are 
indebted for the vast extension of the boundaries of 
human knowledge in the solar system. 

Before we pass these old limits, which for so many 
thousand years were regarded as impassable, we must 
render an account of the great discoveries, whereby it 
became possible to achieve the crowning victories of 
human genius in the planetary regions, and to extend 
these conquests far beyond the limits of solar influence 
into regions of space and among revolving orbs, of which 
the old philosophers had no conception. 



CHAPTER IX 



THE LAWS OF MOTION AND GRAVITATION. 



The Demands of Foemal Asteonomy. — Those of Physical Asteonomy. — 
synopsi8 of the discoveries already made. — questions eemaining to be 
Answered. — Inquiry into Causes. — The Laws of Motion demanded. — 
Eectilineal Motion.— Falling Bodies.— Law of Descent. — Motion of 

PbOJECTILES. — CURVILINEAE MOTION.— FlBST LAW OF MOTION.— SECOND 

Law of Motion. — Momentum of Moving Bodies. — Motion on an Inclined 
Plane. — The Centrifugal Force.— Central Attraction.— Gravitation. 
— Laws of Motion applied to the Planets. — Questions Propounded in 
Physical Astronomy. — Newton's Order of Investigation. — His Assumed 
Law of Gravitation.— Outline of his Demonstration.— Its Importance 
and Consequences.— The Law of Geavitation embraces all the Plan- 
ets and their Satellites. — Gravitation Eesides in eveey Paeticle of 
Matter. 



The discoveries thus far made among the revolving 
worlds dependent on the sun have their origin in a 
rigorous comparison between the actual phenomena pre- 
sented in nature and the hypothetical facts derived from 
an assumed theory. Hipparchus and Ptolemy surpassed 
their predecessors because, on careful examination, they 
discovered that the motion of the sun and moon and 
planets, not being uniform, as had been asserted and be- 
lieved, they explained this irregularity by the hypothe- 
sis of an eccentric position in the central orb, thus 
enabling them to anticipate all the anomalous movements 
known in the age in which they lived. Succeeding dis- 
coveries, adding to the complexity of the theory of eccen- 
trics and epicycles, drove Copernicus to a new center of 



MOTION AND GRAVITATION. 167 

motion in the sun, and this hypothesis, united to the old 
theory, of epicycles, was sufficient to harmonize the then 
known facts of astronomy with the predictions of scien- 
tific men. 

Increased accuracy of observation, however, soon re- 
vealed certain undoubted discrepancies between the abso- 
lute places of the heavenly bodies, as given by instru- 
mental observation, and their places as obtained by 
computation, and after exhausting every possible expe- 
dient to restore harmony between observation and com- 
putation, finding it impossible, Kepler, as we have seen, 
was compelled to abandon the circular theory, as Coper- 
nicus before him had been forced to relinquish the geo- 
centric hypothesis. 

In all this long lapse of many thousands of years the 
human mind has occupied itself exclusively with the 
great problem of framing an hypothesis which would em- 
brace all the phenomena as presented in the heavens. 
It was a question as to where was the center of motion, 
not why it was there ; what was the figure of the plane 
tary orbits, not why this particular figure existed ; how 
the planets deviated from a uniform velocity in their rev- 
olution round the sun, not why they were accelerated 
and retarded ; how the periods of revolution and the 
mean distances were related, not why they were thus re- 
lated. In short, the facts and not the causes occupied 
the exclusive attention of the great astronomers, until the 
science of facts, or formal astronomy, had reached its 
limit, and the mind, having exhausted this field of in- 
vestigation, was compelled to turn its attention to causes 
or to physical astronomy. 

Let us review and condenso the facts thus far de- 
veloped by formal astronomy. 



168 THE LAWS OF 

The planets revolve about the sun as their common 
center of motion in orbits whose figure is nearly, if not 
quite, elliptical. 

Their motion is not uniform, but grows swifter as they 
approach the sun, and loses in velocity after passing their 
perihelion or nearest point to the sun. 

The dimensions of the planetary orbits are not abso- 
lutely invariable. There are slight fluctuations not to be 
overlooked in the periodic times and mean distances. 

The positions of the orbits in their own plane are sub- 
ject to perpetual change, very slow in some of the planets, 
but comparatively rapid in the moon and in the satellites 
of other planets. 

The inclinations of the planes of the planetary orbits 
to a fixed plane are also in a state of fluctuation, some 
angles increasing while others are diminishing. 

The lines of nodes, in which the planes of the orbits of 
the planets intersect the plane of the earth's orbit, are 
not fixed lines. They are found, on the whole, to retro- 
grade, but are sometimes found to advance in the order 
of planetary revolution. 

The moon exhibits anomalous movements, very marked 
and well-defined, and which are evidently outside of her 
elliptic motion, rising above and superior to the general 
law of her revolution. 

The most considerable of these lunar inequalities 
amounts to 1° 20' 30", by which quantity she is alter- 
nately in advance and behind her elliptic place in her 
orbit. This motion was known to the ancients, having 
been discovered by Ptolemy, and was readily appreciable 
by the imperfect instruments employed by the Greek as- 
tronomers. It is known as the moon's evectlon. 

A second inequality, amounting to 1° 4', called the 



MOTION AND GRAVITATION. 169 

moon's variation, was discovered by the Arabians, and 
by them transmitted to posterity, showing the moon's 
motion accelerated in the quadrants of her orbit preced- 
ing her conjunctions and oppositions, and retarded in the 
alternate quadrants. 

A third lunar inequality was called the annual equa- 
tion, a name adopted to express the fact that the moon's 
place in her orbit is for half a year in advance of her 
elliptic place, and for the other half year behind it. 

The line of apsides or longer axis of the lunar orbit 
performs a complete revolution in the heavens in 3232.57 



The line of nodes revolves round the heavens in 
6793.39 days. 

The vernal equinox is also in motion, sweeping round 
the heavens in 25.868 years, while the north pole of the 
heavens revolves round the pole of the ecliptic in the 
same exact period. 

Add to these facts, all discovered by observation and 
reflection, the grand discovery of Kepler, that the squares 
of the periods of revolution are precisely proportional to 
the cubes of the mean distances of the planets, and that 
this and the other laws of Kepler govern the satellites, 
and we have a fair exhibition of the great truths of formal 
astronomy, and it is to answer why theso phenomena 
exist that physical astronomy has been cultivated as a 
science. 

"Why docs a planet continue to revolve about the sun ? 
In case it approach the sun at all, why not continue that 
approach until it be precipitated on the surface of the 
solar orb ? Why do these revolving bodies describe el- 
liptic orbits, with the sun always in the focus of every 
orbit? Why are the deviations from elliptic motion 



170 THE LAWS OF 

what they are ? and how comes it that the elliptic ele- 
ments are in a state of perpetual fluctuation ? Why do 
not the planets fall on the sun, or fly off into space, or 
stop motionless in their orbits ? What holds the earth to 
the sun, or the moon to the earth, so that they never 
part company, and unitedly sweep harmoniously round 
the sun ? What bond unites all the satellites to their 
primaries, and all these primaries to one central orb ? 

Do all these interrogatories admit of a single answer, 
or shall we find these phenomena to spring from diverse 
origins, and due to a variety of causes ? 

Before it was possible to consider any one of these 
grand problems it became necessary to reconstruct the 
old science of mechanics or mechanical philosophy, which 
was contemporaneous with the Greek astronomy of 
Ptolemy, and at the time of Kepler and Galileo exerted 
quite as powerful an influence over the human mind as 
did the doctrines of Ptolemy and Hipparchus. The phil- 
osophy of Aristotle was taught in all the schools, sus- 
tained by the immense influence of professional organiza- 
tion, and received with a fullness of confidence and depth 
of submission which, so far from tolerating doubt, actually 
prohibited inquiry. 

As the planets and their satellites were bodies in mo- 
tion, no advance could be made in the inquiry concern- 
ing causes until the true nature of motion and the laws 
by which it was governed could be determined. These 
laws could only be revealed by accurate thought and ob- 
servation, and would naturally be independent of the 
cause producing the motion. 

The most obvious example of motion is where a heavy 
body is dropped vertically from any height, and falls 
toward the earth. Observation teaches the rectilineal path 



MOTION AND GRAVITATION. 171 

of such a falling body, as well as its direction, which is 
toward the center of the earth. It was a matter of ex- 
periment to determine whether the velocity was uniform 
or accelerated, and if accelerated, observation alone could 
determine the law of acceleration. All this was quite in- 
dependent of the cause producing the original motion, the 
rectilineal direction, the acceleration, and the direction 
toward the earth's center. 

Aristotle had laid down the law of falling bodies, and 
asserted that in case balls of unequal weight were drop- 
ped at the same moment from equal elevations the heavier 
ball would move the swifter, and that the velocity of the 
two balls would be directly proportional to their respect- 
ive weights. It was easy by experiment to prove or dis- 
prove this statement, and Galileo is said to have given 
the first powerful blow to the Greek philosophy, by 
showing experimentally, (by dropping balls of unequal 
weights from the summit of the leaning tower of Pisa.) 
that the velocity of the ball, or the time occupied in the 
fall, was entirely independent of the weight of the 
ball, the resistance of the atmosphere being taken into 
account. 

By measuring the space passed over by a falling body 
in equal intervals of time, it became possible to deter- 
mine the law of descent, and it was thus found that every 
falling body passes through, say, sixteen feet in the first 
second of its full. This is the velocity impressed in the 
first second of time, and were the body to move on with 
the velocity thus acquirod, it would pass uniformly over 
thirty-two feet in the next second of time. But it is 
found that the velocity of every felling body is increasd 
in every second of time by the same precise velocity 
acquired in the first second, and thus in case a cannon 



172 THE LAWS OF 

ball were projected downward at the rate of a thousand 
feet in one second, it would not only pass over one 
thousand feet, but the sixteen additional feet acquired by 
a body falling from a state of rest would be added to 
the thousand feet due to the impulsive force of the gun- 
powder. 

Again, in projecting a body vertically upward, it was 
discovered by experiment tha/t at equal elevations in the 
ascent and descent the velocities were identical, and thus 
whatever might be the cause retarding the ascending 
body, or accelerating the descending one, that cause was 
found to exert its force with a constant energy. 

Galileo was the first fully to develop the facts above 
stated, which facts manifestly began to couple motion and 
velocity with some mysterious cause of acceleration and 
retardation. 

The rectilineal motion of falling bodies naturally led 
to the inquiry as to the line in which a body, receiving a 
single impulse, would move, if entirely free from the influ- 
ence of extraneous forces. A body shot from a gun hori- 
zontally, at the commencement of its motion seemed to 
move in a right line, but a more rigid examination 
showed that (the air as a resisting medium out of con- 
sideration) the bullet commenced to fall at the moment 
of its flight, and actually did fall in one second of time 
through a vertical height precisely equal to the space it 
would have fallen through if dropped from the muzzle of 
the gun. Here, then, was a deviation from a rectilineal 
path accounted for by admitting a constant deflecting 
force precisely equal to that force, wherever it may be 
lodged, or whatever it may be, which produces and ac- 
celerates the velocity of falling bodies. 

As the right line is the most perfect of all lines, and 



MOTION AND GRAVITATION. 173 

as uniform motion in a right line is the simplest of all 
motions,, Galileo conceived the idea that in case a body 
receive a single impulse giving a velocity of any rate per 
second, that the body thus set in motion will move off 
with uniform velocity in a straight line, holding the di- 
rection in which the impulse is applied, and will thus con- 
tinue moving for ever, unless some force or power 
be exerted to change the direction or to destroy the 
velocity. 

This conception or hypothesis could not be proved 
directly from experiment. A ball perfectly hard, round 
and smooth, shot on a level surface like ice, would pre- 
serve its rectilineal path and its initial velocity much 
longer than if opposed by irregularities of surface and 
other resisting causes ; and thus it became manifest that 
as the resistances to motion were diminished, there was a 
nearer positive and experimental approach to the verifica- 
tion of the principle laid down by Galileo, till finally it 
became a settled principle, and was at length dignified as 
the first great law of motion. 

Previous to the discovery of this law the mind had 
never been able to conceive the idea that motion could 
continue after the cause producing it had ceased to act, 
and yet there is no motion produced by human contriv- 
ance, such as the motion of a stone from a sling, or a 
ball from a cannon, in which it is not manifest that the 
force producing the motion ceases its action after the first 
impulse. The sling cannot pursue the stone once liber- 
ated, nor the powder with its expansive power follow the 
ball once released from the gun ; and thus it is clear that 
motion, once generated, survives for a longer or shorter 
time the direct action of the impulsive force. 

So much for rectilineal motion. We are indebted to 



174 THE LAWS OP 

Galileo again for the second law of motion, or the law 
by which we pass from rectilineal to curvilinear motion. 
A ball projected horizontally, as we have seen, soon com- 
menced to fall away from the straight line in which its 
motion commenced. Galileo proved that under the 
united effect of the projectile force, and the force which 
caused it to fall toward the earth, the ball would de- 
scribe a regular curve, called a parabola, which is nothing 
more than an ellipse, whose major axis is infinitely long. 
This curve may be seen in the form of the jet, when 
water or any other fluid spouts from an orifice near the 
bottom of a cylindrical vessel. 

The Florentine philosopher in pursuing this subject 
finally came to generalize the principle involved, and dis- 
covered that if a body in motion at any given rate re- 
ceive an impulse, whose line of direction forms any angle 
with the line of direction of the moving body, it will im- 
mediately take up a new line of direction, according to a 
law which may be thus announced : — 

If two sides of a square or rectangle represent the 
intensities and directions of two impulsive forces 
acting at the same instant, on a body at the angle 
formed by these sides, then the body which, at the 
end of one second, would have been found, under the 
impulse of either force, at the extremity of the side 
representing the force, will neither follow the one side 
of the rectangle nor the other, but will take the direc- 
tion of the diagonal, and at the end of one second will 
be found at the extremity of that diagonal, as may be 
more readily comprehended from the figures below. 

Let F be any impulsive force, such, that acting on the 
material point P, in the direction P B, would project it 
to B in one second of time, and F' be an impulsive force 



MOTION AND GRAVITATION. 



175 



which, acting on the same material point P, in the direc- 
tion P A, would project it to A in one second ; then, in 
case the two forces operate at the same moment on the 
material point P, at the end of one second it will neither 
be found at B nor at A, but will be found at C, the ex- 
tremity of the diagonal of the parallelogram. 





This principle is known as the second law of motion, 
and is also known as the parallelogram of forces. 

In these investigations no account has been taken of 
the weight or mass of the body moved. It was clearly 
perceived that the force exerted by a body at rest press- 
ing upon any support was precisely proportioned to its 
weight, and hence a ball weighing ten pounds would 
bend a spring through ten times the space due to a ball 
weighing but one pound. Aristotle knowing this truth, 
and believing that this pressure downward was the mov- 
ing force, when a body fell freely, asserted the principle 
that a body would fall with a velocity proportioned to its 
weight, which, as we have said, was disproved by Galileo 
in his celebrated experiment at the leaning tower of Pisa. 

It was manifest, however, that when two balls of un- 
equal weight fell from the same elevation, although they 
struck the ground at the same moment, or fell with equal 
velocities, the effect of the blow struck by the heavy 
body was very different from that produced by the lighter 



176 THE LAWS OF 

body. Indeed, it was easy, by experiment, to prove that 
the effect was precisely proportioned to the weight of the 
falling body, and that a body of ten pounds weight would 
strike a blow ten times more powerful than a one pound 
weight after falling through equal heights. It was thus 
seen that to estimate the effect of a blow struck by a 
moving body we must take into account not only the 
velocity but also the weight or mass of the body. The 
same body, with double velocity, doubling its effect, in 
short, the mass multiplied by the velocity, now called 
the momentum, became the true representative of the 
effect produced by the blow struck by a moving body. 

Having reached clear ideas and true laws on these im- 
portant subjects, Galileo gave his attention to the circum- 
stances of motion on an inclined plane. By experiment 
he demonstrated that, if the same body roll down planes 
of the same vertical height, but with different inclinations, 
the velocity acquired on reaching the foot of any one of 
these planes will be independent of the inclination, and 
will always be equal to the velocity due to the verti- 
cal height of the inclined plane. This discovery presented 
the principle of the third and last law of motion, and, 
after much discussion, came to be adopted as a funda- 
mental truth in mechanical science. These laws of mo- 
tion were the result of clear reasoning, based upon 
accurately conducted experiment, and were quite inde- 
pendent of the actual causes producing motion. 

So soon as the knowledge of the second law of motion 
was attained, whereby it became demonstrable that a body 
set in motion by a single impulse, and then operated on 
by a constant power, would describe a curve, it seems 
strange to us, surrounded as we now are by the full illumi- 
nation of a true science, that this principle was not directly 



MOTION AND GRAVITATION. 177 

applied to account for the motions of revolution of the 
celestialorbs. 

Kepler, whose fertile genius, ever active and untiring, 
sought the cause of planetary motion, being ignorant of 
the laws of motion, felt that he must discover and reveal 
some constantly active power operating in the direction 
of the planetary motion so as to keep up the velocity, 
believing that without some such ever-active force the 
planets must of necessity stop. The successors of Kepler 
and of Galileo, for fifty years, or during the first half of 
the seventeenth century, felt strongly the necessity of a 
physical theory of the planetary motions, without attain- 
ing to anything clear or satisfactory. 

That all heavy bodies were in some way attracted by 
the earth, and that the center of attraction was in the 
earth's center, was manifest from the fact that every body 
falling freely, sought the earth's center. But how a 
central force, lodged in the earth or in the sun, could 
operate to keep up a motion of revolution round that 
center, in distant bodies, was the inexplicable mystery. 
The ancients had already remarked that when a stone 
in a sling is whirled rapidly round the head of the 
slinger, a force is developed which powerfully stretches 
the string by which the stone is held. This force was 
called the centrifugal force, and it finally came to be ac- 
cepted that, in all revolving bodies, this tendency to fly 
from the center must be generated, and hence in the 
planets and their satellites a like tendency must exist. 
Reasoning, then, upon the two great facts, that all bodies 
gravitate to the earth, and from analogy all bodies 
equally gravitate to the sun, and that all revolving 
bodies, by the action of the centrifugal force generated 
in their revolution, are disposed to fly from the center 



178 THE LAWS OP 

of motion, Borrelli, of Florence, in 1666, seems to have 
been the first to conceive the idea that in the planets and 
their satellites these two forces might mutually destroy 
or counterbalance each other, and leave the planet in a 
state of dynamical equilibrium to pursue its journey round 
the sun. 

Here we find the germ of the grand theory which at the 
present day embraces within its grasp the entire physical 
universe of God. It was, however, but the germ. Borrelli 
did not pretend to demonstrate the truth of his sugges- 
tion. To accomplish this, it became necessary to demon- 
strate the law of the centrifugal force and the law of 
gravitation, and then to show that the first of these forces, 
as developed by the velocity of revolution of any planet, 
was precisely equal to the force of gravitation exerted by 
the sun at the distance to which the planet was removed. 

The law governing the development of the centrifugal 
force could be investigated experimentally. A cord suf- 
ficiently strong to hold a body suspended from a fixed 
point was not strong enough to hold the same body when 
made to revolve about the point, and, as the velocity of 
revolution was increased, the strength of the cord had to 
be increased. But it was soon found that, with double 
the velocity a cord twice as strong would not retain the 
revolving body. The centrifugal force increased, there- 
fore, in a higher ratio than the simple velocity. By 
further experiment it was discovered that when the veloc- 
ity of the revolving body was doubled, the cord holding 
it must be quadrupled, and when the velocity was 
tripled the cord must be made nine-fold stronger, and 
hence it became finally a fixed principle that the centri- 
fugal force in every revolving body increased with 
the square of the velocity. It remained yet to ascertain 



MOTION AND GRAVITATION. 179 

in what way this force was affected by the distance of 
the revolving body from the center of motion. This was 
accomplished experimentally, and the complete law regu- 
lating the development of the centrifugal force in all re- 
volving bodies having been determined, this force was 
found to increase as the square of the velocity and to de- 
crease directly as the distance from the center of motion 
increased. 

With the knowledge of this important law, we can re- 
turn to the consideration of the planetary revolutions. 
That these bodies were urged directly from the sun by 
the action of the centrifugal force generated by their ve- 
locity of revolution could not be doubted, and to counter- 
balance this tendency to fly from the center of motion 
some force precisely equal and opposite must exist. This 
force was called the gravitating force, or force of grav- 
ity, and the law regulating its intensity remained to be 
discovered. 

Kepler had not foiled to conjecture the existence of 
some such central force lodged in the sun and in the 
earth. He even went further, and conceived the same 
force of attraction to exist in the moon, and finding the 
tides of the ocean to be swayed by that distant orb, ho 
conceived that the same energy which manifested itself 
in a heaving up of the ocean wave, must exert itself with 
equal power on the solid mass of the earth. These, 
however, were mere speculations with Kepler, and even, 
in case he had seriously undertaken to prosecute the re- 
search, the ignorance of the true laws of motion then 
existing would have rendered any success impossible. 
From the days of Kepler to these of Newton this great 
problem constantly occupied the thoughts of the most 
eminent philosophers : AVas the gravitating force whereby 



180 THE LAWS OF 

bodies fell to the earth's surface a constant or variable 
force ? Was this force operative in the distant regions 
of space ? Did its power extend to the moon ? and was 
it there precisely what it should be in order to counter- 
balance the energy of the centrifugal force ? Did this 
same gravitating power dwell in the sun and other plan- 
ets, as well as in the earth ? Did the sun's gravity ex- 
tend to each of the planets, and exert at these different 
distances an energy equal and opposite to the existing 
centrifugal force due to the planet's distance and velo- 
city ? In short, was there a force or energy dwelling in 
every particle of ponderable matter whereby every exist- 
ing particle attracted to itself every other existing par- 
ticle, with an energy proportioned in some way to their 
weights and to the distances by which they were separ- 
ated ? Could such a force, lodged centrally in the sun, 
and operating by any law, convert the rectilinear motion 
of a body darted into space by a single impulse into ellip- 
tical motion, and at the same time, at every point in 
the elliptical orbit, precisely counterpoise the centrifugal 
force due to the planet's distance and velocity? Could 
the same force, governed by the same laws and lodged in 
the primary planets, control the movements of their 
satellites ? These were the grand inquiries which en- 
grossed the attention of the generation of philosophers 
which nourished from the time of Kepler and Galileo up 
to the era rendered immortal by the grand discovery of 
the law of universal gravitation by Newton. 

Newton's discovery of the laav of gravitation. 
— We are now prepared to consider the train of reason- 
ing employed by the English philosopher in his re- 
searches for the law of gravitation. Many astronomers 
before Newton had conjectured that the force exerted by 



MOTION AND GRAVITATION. 181 

the sun on the planets, and by the primaries on their 
satellites, decreased as the square of the distance in- 
creased^ or followed the law of the inverse ratio of the 
square of the distance. This was inferred from the con- 
sideration of fact, that this attractive energy, called grav- 
ity, was lodged in the center of the sun, and issued from 
that center in all possible directions, like light emanating 
from a luminous point. As the distance increased from 
the center the force would become less intense, and might 
follow the law of the decrease in the intensity of light, 
which was well known by experiment to be the inverse 
ratio of the square of the distance. It was one thing to 
conjecture this to be the law regulating the force of grav- 
ity, but quite a different thing to demonstrate the truth 
of such a conjecture. 

The investigation as pursued by Newton, and the dis- 
coveries made by that distinguished philosopher, followed 
progressively in a series of distinct propositions, the de- 
monstrations of which were reached at different periods. 

First, Newton demonstrated that, assuming the third 
law of Kepler as a fact derived from observation, as a 
consequence of this fact, (combined with the law of the 
centrifugal force,) the gravitation of the planets to the sun 
must diminish in the inverse ratio of the square of their 
respective distances. This demonstration was accom- 
plished by a train of mathematical reasoning, of which 
we will not stop to give any account at present. It was 
based, however, on the assumption that the planetary 
orbits were circles, and hence did not meet the case of 
nature. 

The second stop was to prove that in ease a planet re- 
volved in an elliptical orbit, that at every point of its 
revolution the force exerted on it by the sun, or iU 



182 THE LAWS OF 

gravitation to tne solar orb, was always in the inverse 
ratio of the square of its distance. This was equivalent 
to proving that if a body in space, free to move, received 
a single impulse, and at the same moment was attracted 
to a fixed center by a force which diminished as the 
square of the distance at which it operated increased, 
such a body, thus deflected from its rectilineal path, would 
describe an ellipse, in whose focus the center of attrac- 
tion would be located. 

The third step in this extraordinary investigation was 
to demonstrate that, this gravitating power lodged in the 
sun, and controlling the planetary movements, was iden- • 
tical with that force exerted by the earth over every fall- 
ing body, and extending itself to the moon, decreasing in 
intensity in proportion as the square of the distance in- 
creased, and thus opposing itself as a precise equipoise 
at every moment to the effect of the centrifugal force 
generated by the motion of this revolving satellite. 

The fourth step required the philosopher to demon- 
strate that not only did the planets gravitate to the sun, 
and the satellites to their primaries, but that each and 
every one of these bodies, sun, planet and satellite, 
gravitated to the other, and that each attracted the other 
by a force which varied in the inverse ratio of the square 
of the distance. But here it was found that another mat- 
ter had to be taken into account. The energy of gravi- 
tation did not depend alone on distance. The power 
exerted by the sun on the planet Jupiter was vastly 
greater than that exerted by Saturn, though Jupiter 
was nearly equidistant from these two bodies when in 
conjunction with Saturn. Newton proved that the 
power of gravitation lodged in any body depended on the 
mass or weight of the body, and hence if the sun weighed ) 



MOTION AND GRAVITATION. 183 

a thousand or ten thousand times as much as a planet, 
its energy at equal distances would, by so much, exceed 
that put forth by the smaller orb. 

The fifth and final step in this sublime, intellectual 
ascent to the grand law of the physical universe, re- 
quired the philosopher to prove that the force, power, or 
energy, now called gravitation, lodged in the sun, plan- 
ets and satellites, pervaded equally every constituent 
particle of each of these bodies, and did not dwell alone 
in the mathematical center of the sun or planet. In 
short, it was required to show that every ponderable par- 
ticle of matter in the whole universe possessed and 
exerted this power of attraction in the direct 'proportion 
of its mass, and in the inverse ratio of the square of 
the distance at which its energy was manifested. 

In case these propositions could be clearly and satis- 
factorily demonstrated, an instant and absolute revolution 
must commence in the whole science of astronomy, and 
the business of future ages would be nothing but the 
verification of this one grand controlling law, in its appli- 
cation to the phenomena presented in the movements not 
only of the sun's satellites and their attendants, but in 
those grander schemes of allied orbs revealed by tele- 
scopic power in the unfathomable regions of the sideral 
heavens. 

We shall now exhibit an outline of the demonstration 
accomplished by Newton to prove that the law of uni- 
versal gravitation, as above announced, was the exact law- 
according to which the earth exerted its attractive power 
on the moon, and held this globe steady in its orbit 

The intensity of any force, as we have seen, is measured 
by the velocity it is capable of producing in a heavy 
particle in any unit of time, as one second. The earth's 



184 



THE LAWS OF 



gravity at the surface is measured then by the space 
through which a body falls in a second of time, which 
space (as experiment demonstrates) is about sixteen feet. 
In case it were possible to measure with absolute precision 
the space through which a body falls at the level of the 
sea and then at the summit of a mountain (if there were 
any such) 4,000 miles high, it would be easy to verify 
the truth of the assumed law by actual experiment ; but 
no mountain exists on the earth's surface whose height is 
comparable with the length of the earth's radius, and as 
it is absolutely impossible to ascend vertically above the 
earth to any considerable height, Newton soon saw that 
no means existed on the surface of the earth whereby 
the truth or falsehood of his assumed hypothesis might 
be ascertained. In this dilemma he conceived the idea 
that the moon might be employed in the experiment, not 
by arresting her motion and dropping her literally to the 
earth, but by considering the earth's attractive power as 
the cause of her deflection from a rectilineal movement. 
In one sense the moon is perpetually falling to the earth, 
as may be readily comprehended from an examination 
of the figure below : — 



M M 




MOTION AND GRAVITATION. 185 

Let E represent the earth's center, M a point of the 
moon's orbit, in which she is at rest with no force what- 
ever operating on her. Now let an impulse be applied to 
the moon, in the direction M M'", tangent to the orbit, or 
perpendicular to the line M E, and with such intensity 
that at the end of one second of time the moon will be 
found at M'". Return the moon to M, and conceiving 
her to drop toward the earth, under the power of the 
earth's attraction, let us suppose that she passes over the 
distance M M7 in one second. In case the moon be brought 
back again to M, and the impulse be now applied, and at 
the instant the moon darts off along the straight line 
MM'", she is seized by the earth's attractive power, 
and, bending at once under these conjoined influences, she 
commences her elliptical orbit, and at the end of one 
second is found at M", passing over a sort of curvilinear 
diagonal of the parallelogram formed on the two sides 
M W" and M M'. Now, it is manifest that the line 
M'" M" is equal to M M', that is, that the amount by 
which the moon is deflected from a right line is precisely 
the amount by which she falls to the earth in one second 
of time. The problem then resolved itself into a com- 
putation of the line MM', or the distance through which 
the moon ought to fall in one second, in case the assumed 
law of gravition be true, and the exact measurement in- 
strumentally of the distance M"' M", the space through 
which the moon did fall in one second. An exact equal- 
ity between these two quantities would establish the law 
of the decrease of the earth's power of attraction to be in 
the inverse ratio of the square of the distance. 

It will be seen that to compute how far a body would 
fall in ono second, when removed to the moon's distance, 
in case the earth's gravity be diminished as the square of 



186 THE LAWS OP 

the distance increases, is a matter involving no difficulty 
or uncertainty whatever, in case we know what the moon's 
distance is. In like manner, to obtain the space through 
which the moon actually falls to the earth in one second 
or minute of time, knowing her distance, admitting her 
orbit to be circular, and assuming that we know her 
periodic time, is a problem of easy solution. 

The chief difficulty lay in accomplishing an accurate 
determination of the moon's distance from the earth, a 
matter which could not be determined without an accu- 
rate knowledge of the earth's diameter or radius, as we 
have already seen. 

"When Newton commenced his investigation the meas- 
ures which had been executed of an arc on the meridian, 
whereby the entire circumference of the earth might be 
obtained and its diameter computed, were comparatively 
imperfect, yielding only an approximate value of the 
earth's radius. As this quantity was the unit employed 
in the measure of. the moon's distance, any error in its 
value would be repeated some sixty times in the value 
of the moon's distance, and as the gravity of the earth 
was assumed to decrease as the square of the distance in- 
creased, we perceive that any error in the radius of the 
earth would operate fatally on the solution of this problem, 
involving the fate of the most comprehensive and far- 
reaching hypothesis ever conceived by the human mind. 

Unfortunately for Newton, the. value of the earth's 
diameter, employed in his first computations, was in 
error, and in executing the computation the values of the 
space through which the moon ought to fall, and the 
space through which she did fall, were discrepant by an 
amount equal to the sixth part of the entire quantity. 
So great a disagreement was fatal to the theory in the 



MOTION AND GRAVITATION. 187 

truth-loving and exact mind of Newton, and for many 
years he abandoned all hope of demonstrating the truth 
of his favorite hypothesis. Still his mind was in some 
way powerfully impressed with the conviction that he 
had divined the true law of nature, and he returned again 
and again to his computations in the hope of removing 
the discrepancy by detecting some numerical error. It 
was impossible, however, to find an error where none ex- 
isted, and for a time the great philosopher abandoned all 
hope of accomplishing this, the grandest of all the efforts 
of his own sublime genius. Such was the condition of 
this investigation when a new determination of the value 
of the earth's diameter was accomplished in France, by 
the measurement of an arc of the terrestrial meridian. 
Having obtained this new value of the earth's diameter, 
Newton resumed once more the consideration of the pro- 
blem which had so long occupied his thoughts. The 
new value was substituted for the old — the moon's distance 
being now accurately known — the space through which 
a body would fall in a unit of time, under the power 
of gravitation, when removed to this new distance, was 
rapidly computed. In like manner the distance through 
which the moon must actually fall was also obtained by 
using the new value of the earth's diameter. 

It would be impossible to form any just idea of the in- 
tense emotions which must have agitated the mind of tlio 
English philosopher while engaged in bringing these last 
computations to a close. Upon a comparison of the re- 
sults now reached there hung consequences of incalcul- 
able value. No less than nineteen years of earnest study, 
of profound thought, and of the most laborious investi- 
gation, had already been exhausted on this grand pro- 
blem, and now within a few minutes tho fate of the 



188 THE LAWS OF 

theory and the fame of the astronomer were to be for 
ever fixed. No wonder, then, that we are told that even 
the giant intellect of Newton reeled and staggered under 
the tremendous excitement of the moment; and seeing 
that the figures were so shaping themselves as inevitably 
to destroy the discrepancy which had so long existed, 
overcome by his emotions, Newton was compelled to ask 
the assistance of a friend to finish the numerical compu- 
tation, and when completed it was found that the space 
through which the moon did fall in a unit of time was 
identical with the space through which she ought to fall, 
in case her movements were controlled by a power lodged 
in the earth's centre, and decreasing in energy as the 
square of the distance at which it operated was in- 
creased. 

Here was presented the first positive proof of the 
prevalence of that universal law of mutual attraction 
which energizes every particle of ponderable matter ex- 
isting in the universe. The earth's power of attraction 
was thus shown to exert itself according to a fixed law, 
in deflecting the moon from the rectilineal path it would 
otherwise have followed, converting its motion into one 
of revolution, giving to its orbit the elliptical form, and 
maintaining at every point of its revolution the most 
exact and perfect equilibrium. 

It may, perhaps, seem extraordinary that so much con- 
sequence should have been attached by Newton to the 
successful demonstration of this particular problem. If 
he had already shown that the sun's attraction upon the 
planets followed the law of the inverse ratio of the square 
of the distance, and that the same law prevailed in the 
attraction of the sun upon any one planet at different 
points of its orbit, why regard as a matter of such 



MOTION AND GRAVITATION. 189 

high value the demonstration of the fact that the earth's 
attraction upon the moon was governed by the same 
identical law. The answer, I think, may be readily 
given. 

The great problem was this : Does one law reign su- 
preme over all the ponderable masses of the physical 
universe, or are there many subordinate laws holding their 
sway in the diverse systems and bodies which are revealed 
by sight ? Might it not be that the sun would attract 
the planets according to one law, while the planets might 
attract their satellites according to a different law ? By 
demonstrating that the earth controlled the moon by the 
same precise power whereby the sun controlled the plan- 
ets, it was demonstrated that the ponderable matter of 
the earth was identical in character with the ponderable 
matter of the sun, and from this it followed that as the 
earth was one of the planets controlled by the power of 
gravitation of the sun, so likewise the other planets 
which were controlled by the same power must be com- 
posed of ponderable matter, governed by the same laws 
which reign in the sun and earth. 

We perceive, then, that this demonstration, executed 
by Newton, in which he proves that the earth's attrac- 
tion controlled the moon, deserves the high rank which 
he has assigned it, for it is nothing less, when conjoined 
with his previous demonstrations, than proving that every 
globe which shines in space, planet and satellite, and 
sun, are but parts of one mighty system linked together 
by indissoluble bonds, forming one grand scheme, in 
which each exerts its influence upon the other, the whole 
controlled by one supreme and all-pervading law. 

It only remained now to extend by demonstration the 
empire of the law of universal gravitation over eaeh 



190 THE LAWS OF 

particle of matter composing the several worlds. This 
was a problem of no ordinary difficulty ; for Newton soon 
discovered that in case a mass of ponderable matter were 
fashioned into the shape of a sphere, that for all the 
purposes of computation it would be safe to consider the 
entire globe as concentrated in one single point at the 
centre. Observation taught that all the planets, as well 
as their satellites, were bodies of globular form, and hence 
in applying the law of universal gravitation to the study 
and computation of their movements, the same results 
would be obtained by admitting the whole force of attrac- 
tion belonging to these bodies to be concentrated in their 
central points, or to be distributed among the different 
particles composing the globe. To show, then, that 
gravity resided in every particle composing a globe, and 
not in its central point, was an impossible thing, so far 
as the distant worlds were concerned. In the world which 
we inhabit, however, and where we can study its indi- 
vidual portions, and where we can penetrate to certain 
depths toward its center, it may not be impossible to 
learn whether the power of gravitation dwells in every 
ponderable atom which goes to make up the entire 
earth, or whether it is concentrated in the central point 
alone. 

There are several methods which may be employed to 
ascertain whether there be any power of attraction in 
separate portions of the earth or in the crust of the earth. 
The effect of a high mountain on the direction of the 
plumb-line, (which at the level of the sea holds a direc- 
tion perpendicular to the surface,) in causing it to devi- 
ate from this direction, may be measured with suffi- 
cient accuracy to demonstrate the power of attraction 
existing in the mountain. Such an experiment, however, 



MOTION AND GRAVITATION. 191 

could not be employed to demonstrate that the law of 
universal gravitation prevailed among the particles com- 
posing the mountain, it would only show that there was 
a power of attraction exerted by the mountain, and in 
case we knew the exact amount of deviation of the plumb- 
line from the vertical, and the magnitude of the moun- 
tain, as well as the law according to which its attractive 
power was exerted, we could then obtain the quantity of 
matter contained in the mountain mass. 

A second method may be employed to ascertain 
whether the whole power of gravitation is lodged in the 
center of the earth or is distributed among all its constit- 
uent particles. If it were possible to penetrate toward 
the earth's center, a thousand miles below the surface, 
and there drop a heavy body, and measure the space 
through which it falls in a unit of time, if this measured 
space should be identical with that over which the body 
ought to fall, on the supposition that its velocity de- 
pended simply on its distance from the center, such an 
experiment would demonstrate that the earth's gravitat- 
ing force resided in the central point alone ; this experi- 
ment cannot be performed in the exact manner announced, 
but it can be, and has been substantially performed, with 
very great delicacy, in the following manner : 

It is found that a pendulum of given length will vibrate 
seconds at the equator of the earth. If this pendulum 
be removed nearer to the earth's center by carrying it 
toward the poles, the pow>r of gravitation producing its 
vibration thorcby growing more intense, the pendulum 
will vibrate more than sixty times in a minute, and thus 
the number of vibrations in a given time becomes a very 
exact means of measuring the distance of anv point on 
the earth's surface from its center. These experiments, 



192 THE LAWS OF 

however, are performed upon the earth's surface. If, in- 
stead of removing the pendulum from the equator toward 
the poles, and thereby reducing its distance from the 
earth's center, this distance were reduced by the same 
amount by transporting the pendulum vertically down- 
ward into a deep mine — if distance alone from the center 
be the cause affecting the time of the vibration of the 
pendulum — then the number of vibrations in a unit of 
time will be the same in the mine as at a point on the ex- 
terior equidistant from the earth's center. When this 
experiment comes to be performed it is found that there 
is a great difference between the number of vibrations in 
the interior, when compared with the number of vibra- 
tions at the exterior, at equal distances from the center, 
in any unit of time, say a mean solar day, clearly de- 
monstrating that the matter of the earth, lying above the 
pendulum located in the mine, produces a very sensible 
and powerful effect upon the number of its vibrations. 

Here, again, we find it impossible, from this experi- 
ment, to determine the exact law which regulates the at- 
tractive power of the individual particles composing the 
earth, but we do demonstrate the fact that the earth's 
gravity is not concentrated at its center, but dwells, ac- 
cording to some law, in all the atoms which compose its 
mass; and this law, we shall prove hereafter, is none 
other than the great law of universal gravitation. 

It is impossible to form a just idea of the vast import- 
ance which attaches to the grand discovery of Newton. 
It worked out, instantly and absolutely, a complete rev- 
olution in the whole science of astronomy. Previous to 
the discovery of the law of universal gravitation all the 
observations upon the stars and planets, which had been 
accumulating for so many centuries, could only be re- 



MOTION AND GRAVITATION. 193 

garded as so many isolated facts, having no specific re- 
lation the one to the other. The planets were indepen- 
dent orbs, moving through space in orbits peculiar to 
themselves, and only united by the single fact that the 
sun constituted the common center of revolution. The 
discovery made by Newton converted this scheme of iso- 
lated worlds into a grand mechanical system, wherein 
each orb was dependent upon every other, each satellite 
affecting every other, and the whole complex scheme 
gravitating to the common center, which exerted a pre- 
dominant power over each and every one of these revolv- 
ing worlds. 

Those eccentric bodies which we denominate comets, 
whose abrupt appearance in the heavens with their glow- 
ing trains of light, whose rapid movements and sudden 
disappearance have excited such a deep interest in all 
ages of the world, were found not to be exempt, as we 
shall hereafter show, from the empire of gravitation. 



CHAPTER X. 



THE LAWS OF MOTION AND GRAVITATION APPLIED TO 
A SYSTEM OP THREE REVOLVING BODIES. 



System of two Bodies. — Quantities Required in its Investigation.— 
Five in Number. — Sun and Earth. — Sun, Earth and Moon, as Systems 
op Three Bodies. — Thr Sun supposed Stationary. — Changed Figure op 
the Moon's Orbit. — Sun Eevolving Changes the Position of the Moon's 
Orbit. — Solar Orbit Elliptical. — Effects Resulting from the Inclina- 
tion of the Moon's Orbit.— Moon's Motion above and below the Plane 
op the Ecliptic— Revolution of the Line of Nodes.— Sun, Earth and 
Planet, as the Three Bodies. — Perturbations Destroy the Rigor of 
Kepler's Laws.— Complexity thus Introduced.— Infinitesimal Analy- 
sis. — Difference between Geometrical and Analytical Reasoning. 



We shall now present, as clearly as we can, with- 
out the aid of mathematical reasoning, the application 
of the laws of motion and gravitation to the circum- 
stances arising in a system of three bodies mutually 
affecting each other. We will commence even with a 
simpler case, and suppose a solitary planet to exist, sub- 
jected to the attractive power of one sun, and that these 
are the only bodies in the universe. Let us consider 
what quantities are demanded to render it possible for 
the mathematician to take account of the circumstances 
of motion which will belong to this solitary world. 

First of all, it is evident that the quantity of matter 
contained in the sun, or its exact weight, must be known, 
for the energy or power of the sun varies directly as its 
mass, and two suns, so related that the weight of one is 
tenfold greater than that of the other, the heavier one 



MOTION AND GRAVITATION. 195 

will exert a power of attraction tenfold greater than the 
lighter one. 

In the second place, we must know the distance of the 
planet from the sun, for the power of the sun's attrac- 
tion decreases as the square of the distance at which it 
operates increases; so that if at a distance of unity it 
exerts an attractive force which we may call one, at a 
distance two this force will be diminished to one-fourth ; 
at a distance three to one-ninth ; at a distance four to 
one-sixteenth ; at a distance ten to the one hundredth part 
of its first value. 

In the third place, the mass or weight of the planet 
must be known ; for not only does the sun attract its 
planet, but in turn the planet attracts the sun, and the 
intensity of this attraction, which affects the motion of 
the planet as well as that of the sun, depends exclusively 
upon the mass or weight of the planet. 

In the fourth place, we must know the intensity of the 
impulsive force which is employed to start the planet 
in its orbit, for upon the intensity of this force will the 
initial velocity of the planet depend, and we see readily 
that the form of the orbit as to curvature will depend 
upon the initial velocity. The greater this velocity the 
more nearly will the curvature of the orbit coincide with 
the straight line in which the planet would have moved 
in case it had been operated upon by the impulsive 
force alone. 

In the fifth place, before we can completely master 
the circumstances of motion to the planet, we must know 
the direction in which the impulse is applied, tor upon 
this direction it is manifest that the figure of the orbit 
will depend. If the impulsive force be applied in a direc- 
tion passing through tho sun's centre, and toward the 



196 THE LAWS OF 

sun, it is clear that the planet will simply fall to the 
sun in a straight line. If it met with no resistance it 
would pass through and beyond the sun's center until 
its velocity would be entirely overcome by the attraction 
of gravitation, when it would stop, fall again to the sun, 
and thus vibrate for ever in a right line. In case the 
direction of the impulse is oblique to the line joining the 
planet and the sun, (the angle falling within certain 
limits of value,) then the planet will describe an ellip- 
tical figure in its revolution around the sun, and will re- 
turn precisely to the point of departure to repeat the same 
identical curve, with the same velocities precisely at each 
of the points of its orbit, in the same exact order for 
ever. In examining the peculiarities which distinguish 
the movements of this revolving body, we shall find as a 
necessary consequence of the laws under which it moves 
that its motion must be slowest at that point of its orbit 
where it is furthest from the sun. Leaving this point 
as it approaches the sun, its velocity must rapidly in- 
crease, and will reach its maximum at the perihelion of 
its orbit, where, being nearest to the sun, it will move 
with its swiftest velocity. Receding now from the center 
of attraction it will lose its velocity by the same de- 
grees with which it was augmented, and will again pass 
its aphelion with its slowest velocity. Thus we per- 
ceive that the movements of a single planet revolving 
about the only sun in existence are marked with great 
simplicity; and in case the mathematician knows pre- 
cisely the five quantities already named, viz : the sun's 
mass, the planet's distance, the planet's mass, the in- 
tensity of the impulsive force, and the direction of this 
force, it is not at all difficult to determine all the cir- 
cumstances of motion of the planet, and to predict its 



MOTION AND GRAVITATION. 197 

place in its orbit with absolute precision at the end of 
ten thousand revolutions. 

We will not at present attempt to show how these five 
quantities may be obtained. These determinations be- 
long to the department of instrumental astronomy, a 
subject which will be treated after closing what we have 
to say on the application of the law of gravitation to the 
movements of a system of three bodies. 

In case the planets had been formed of a material such 
as to be attracted by the sun, but not to attract each 
other, and if the satellites had been composed of a mate- 
rial such as to be attracted by their primaries only, then 
the elements of the orbits of all these revolving bodies 
would have remained for ever absolutely invariable. So 
soon, then, as accurate observation should have furnished 
the five quantities required in determining the circum- 
stances of motion in any revolving body, mathematical 
computation would have fitted an invariable orbit to each 
one of these bodies, and would have furnished by calcu- 
lation the exact place of each one of these bodies in all 
coming time. The whole system would have been one 
of perfect equilibrium, and although complexity would 
have presented itself apparently in the interlacing revo- 
lutions of these revolving worlds, yet absolute simplicity, 
combined with short periodical changes, would have re- 
stored each one of these bodies to the exact position occu- 
pied when first launched in its orbit. 

This, however, is not the case of nature. The sun 
not only attracts the planets, but also attracts their 
satellites. The primary planets not only attract their 
satellites, but attract each other: and thus not a single 
body exists in the whole universe which is not depend- 
ent upon every other. 



198 THE LAWS OP 

We have already seen that in case the sun with one 
planet were the only objects in existence, that having 
traced the planet in one single revolution round the sun, 
the variations of motion thus developed would be repeated 
without the slightest change in any succeeding revolu- 
tion for all coming time. 

Suppose this solitary planet to be the earth, and 
that from a knowledge of the weight of the sun, the dis- 
tance of the earth from the sun, the weight of the earth, 
the intensity of the impulsive force, and the direction in 
which that force is applied to start the earth in its orbit, 
we determine the elements of its orbit. The form of 
this orbit, its magnitude and position in space will re- 
main absolutely invariable, and the changes of motion 
in the first revolution will be repeated exactly in all 
succeeding revolutions. Let us now add to our system 
of two bodies a third body, as the moon. In case the 
sun had no existence, or was removed to an infinite dis- 
tance, then the circumstances of motion in the moon, 
once determined, would remain absolutely invariable, but 
the moment we unite the three bodies, the sun, earth 
and moon, into a system of three orbs, mutually depend- 
ent upon each other, the perfection and simplicity which 
marks a system of two bodies is for ever destroyed, and 
modifications are at once introduced into the motion of 
the earth revolving around the sun, and also into that 
of the moon revolving around the earth, of an exceedingly 
complex and difficult character, and requiring the high- 
est developments of mathematical analysis to grapple suc- 
cessfully with this great problem of the three bodies. 

The solution of this problem has never been positively 
accomplished, but approximations of wonderful delicacy 
have been reached by the successors of Newton, so that 



MOTION AND GRAVITATION. 199 

for all practical purposes in astronomy this approximate 
solution may be fairly regarded as absolute. 

As the plan laid down in this work does not admit the 
use of any but the simplest mathematical elements, we 
shall only trace out, in general terms, the consequences 
which must follow from the introduction of a third body 
into a system of two revolving orbs, and, for the purpose 
of fixing our ideas, we will suppose the earth and moon 
to be our two bodies. The moon's orbit, in magnitude, 
and figure, and position, is supposed to be known; her 
period of revolution and the circumstances of her motion 
in her orbit are also supposed to be accurately determined. 
The earth being fixed in position, and the moon perform- 
ing her revolution under the laws of motion and gravita- 
tion, let us now add to this simple system a third body, 
the sun; and to render our investigation as simple as 
possible, we will adopt the hypothesis that the earth con- 
tinues at rest, but that a new force, namely, the sun's 
attraction, now commences to exert its influences upon 
the moon. In order still further to simplify the case, 
let us suppose the sun's center to be situated in the pro- 
longation of the longer axis of the moon's orbit, and 
that the moon, in passing through her aphelion, will 
cross the line joining the centers of the earth and sun. 
Under this configuration it is clearly manifest that the 
figure of the moon's orbit will be changed, because the 
attractive power of the sun will certainly increase tho 
distance to which the moon travels from the earth, for 
the velocity with which the moon moves away from her 
perihelion point will be reinforced by the attractive power 
of the sun, and thus her aphelion distance will be in- 
creased. By the same reasoning, it will appear that 
her perihelion distance will be somewhat diminished, and 



200 THE LAWS OF 

thus tbe longer axis will be increased in length, and the 
period of revolution of the moon will, in like manner, be 
increased. 

These changes having been once accomplished, and the 
moon having taken up her new orbit under the action of 
the new forces, so long as these forces remain constant, 
that is, so long as the sun remains fixed in position, the 
new orbit will remain as invariable as did the old before 
the introduction of the sun. All the changes accom- 
plished by the sun's power, whereby the new orbit is 
made to differ from the old, are called, in astronomy, 
perturbations, and the sun is called the disturbing body. 

Let us now suppose the sun, retaining its distance from 
the earth, to start from its position on the prolongation of 
the longer axis of the moon's orbit, and to commence a 
revolution around the earth in a circular orbit, lying in 
the plane of the moon's orbit. A little reflection -will 
show us that the moment the disturbing body commences 
to move, the direction of its attractive power upon the 
revolving moon will begin to change ; a new set of 
disturbances will now commence, not affecting the new 
figure of the moon's orbit, but changing the position of the 
principal lines of the orbit in its own plane ; for it is 
clearly manifest that the strongest power will be exerted 
to draw the moon away from the earth on the line join- 
ing the centers of the earth and sun ; and hence the 
aphelion point of the moon's orbit will necessarily try 
to follow this moving line. The subject will be made 
plainer by an examination of the figure below, in which 
E represents the earth in the focus of the moon's 
orbit, S the place of the sun on the prolongation of 
P M the longer axis, P the perigee, and M the apo- 
gee of the moon's orbit. In case the sun be removed 



MOTION AND GRAVITATION. 



201 



to S', and there remain stationary, it is manifest that 
each time the moon crosses the line E S' it will be sub- 
jected to the most powerful influence to draw it away 
from the earth at E ; and in case the sun remain station- 



E 



ary for a sufficiently long time at each of the moon's 
revolutions, the point M will approach M', and finally it 
will actually fall on M', where it will remain fixed, so 
long as the sun is stationary. 

In case, however, the sun again advances in the same 
direction, the apogee of the moon will again advance, and 
should the sun, by successive steps, slowly perform an 
entire revolution, pausing at each step sufficiently long for 
the moon's apogee to come up to the line joining the 
centers of the earth and sun ; when the revolution of the 
sun shall have been completed the revolution of the 
moon's apogee will, in like manner, have been finished. 

If, instead of supposing the sun to advance by successive 
steps, we admit his uniform progress, it is clearly mani- 
fest that in each revolution of the moon, the apogee of her 
orbit must advance a certain amount in the direction of 
the sun's motion, and, in the end, a complete revolution 
of the moon's apogee will be accomplished under the dis- 
turbing influence of the sun's attraction. 

9* 



202 THE LAWS OF 

We have seen that if the sun were stationary his 
disturbing power would only go to change the figure of 
the moon's orbit, leaving the direction of the longer axis 
undisturbed. The revolution of the sun in a circular 
orbit by slow degrees accomplishes an entire revolution 
of the apogee, or of the line of apsides, and thus, in case 
the line of apsides should perform its revolution in a 
period which shall be an exact multiple of the period of 
the sun's revolution, then at the end of one such cycle 
the moon will have passed through all the changes which 
can arise from the disturbing influence of the sun. These 
changes will therefore be strictly periodical, and in the 
end the moon will return to its first position, and will re- 
peat the same identical changes forever. 

We will now consider the solar orbit to be elliptical. 
This involves, by necessity, a perpetual change in the 
sun's distance, and as his disturbing power varies in in- 
tensity inversely with the square of his distance, it is 
manifest that this variation in the disturbing force will 
introduce a corresponding variation into the figure of the 
moon's orbit. If the sun be supposed to advance toward 
the earth and the moon, in the direction of the line of 
apsides, its disturbing power would be exerted to draw 
the moon further from the earth the nearer the sun ap- 
proached ; in other language, to increase the magnitude 
of the moon's orbit and the period of her revolution. 
This action will be varied in case the sun recede from 
the earth along the same line, and if this approach and 
recess were made by successive steps, at intervals suf- 
ficiently long to allow the moon's orbit to assume a fixed 
form, then one vibration of the sun advancing and re- 
ceding through equal space, would work out a series of 
changes in the form of the moon's orbit identical with 



MOTION AND GRAVITATION. 203 

those accomplished by each successive vibration, while in 
all these changes the direction of the line of apsides 
would remain fixed. 

If now we suppose the advance and recess of the sun 
to be effected by its revolution in an elliptic orbit, then 
We shall find the changes of figure in the moon's orbit, 
just noticed, as due to the sun's change of distance, will 
be combined with an advance and final complete revolu- 
tion of the line of apsides ; and admitting the figure of 
the sun's orbit to remain unchanged, and the principal 
axis of its orbit to remain fixed forever in position, a time 
will come when the sun will have been presented to the 
moon in every possible position, and all the changes in 
the figure of the moon's orbit, and the revolution of the 
line of apsides of the moon's orbit, due to the revolution 
of the sun in his orbit, will have been accomplished. The 
moving bodies return to their primitive points of depart- 
ure, and a new cycle of changes begins, to be repeated, in 
the same order forever. 

Thus far we have supposed the line of apsides of the 
sun's orbit to remain fixed in position and unchanged in 
length. It is manifest that a revolution of the line of 
apsides of the sun's orbit, definite in period and fluctua- 
tions in its length also periodical, would introduce addi- 
tional fluctuations in the moon's motion, and in the 
length and position of the principal axis of her orbit. 
But while we rise in complexity, and while the periods 
requisite for effecting all these changes expand into ages, 
we still recognize the great fact that periodicity re- 
mains, and that in the end, at the termination oi' a vast 
cycle, the revolving bodies must return again to their 
points of departure to repeat the same identical changes 
through endless ages. 



204 THE LAWS OF 

In all our reasoning thus far we have supposed that 
the three bodies under consideration always lie in the 
same plane ; in other language, that the planes of the 
orbits of the moon and earth coincide. This, however, 
is not the case of nature. As we have already seen, the 
moon's orbit is inclined to the plane of the ecliptic under 
an angle of about 5° — the line of intersection of the 
two planes being called the line of the moon's nodes, 
which line must, of course, always pass through the earth's 
center. 

We shall now proceed to take this inclination into 
consideration, and ascertain whether the sun's disturbing 
force has any, and if any, what effect on the position of 
the line of nodes, and on the inclination of the moon's 
orbit. For this purpose let us suppose the earth to be 
stationary, and that the line of nodes of the moon's orbit 
holds a position perpendicular to the line joining the 
centers of the earth and sun, and that the moon starts 
from her ascending node to describe that portion of her 
orbit lying above the plane of the ecliptic. The power 
of attraction of the sun will manifestly exert itself in 
such manner as to cause the moon to deviate from its 
old orbit and to describe a new orbit, which will lie in 
all its points a little nearer to the plane of the ecliptic. 
The moon will not, therefore, rise in this superior part 
of her orbit as high above the plane of the ecliptic as she 
did before her motion was disturbed by the sun ; and in 
descending to pass through her node she will clearly reach 
the plane of the ecliptic quicker than she did when un- 
disturbed, and pass through her node at a point nearer 
to herself than that occupied by the former node : in 
other language, the old node comes up to meet the ad- 
vancing moon, and thus takes up a retrograde motion. 



MOTION AND GRAVITATION. 205 

Let us now examine the motion of the moon in that 
portion of her orbit lying beneath the plane of the eclip- 
tic and most remote from the sun. Here the sun's dis- 
turbing influence will be diminished somewhat, in conse- 
quence of the increased distance at which it operates, but 
its effect will manifestly be to cause the moon to descend 
more rapidly and to reach a lower point beneath the 
ecliptic than when undisturbed, increasing the inclination 
of the plane of the orbit, and causing the moon to reach 
her ascending node at a point earlier than when undis- 
turbed, and thus producing a retrocession or retrograde 
motion of the line of nodes. Thus it appears that in the 
long run the sun's disturbing influence will tend to 
change within certain limits the angle of inclination of 
the moon's orbit ; and, indeed, if the earth were fixed in 
position, would finally destroy this inclination entirely, 
reducing the plane of the moon's orbit to absolute coinci- 
dence with that of the earth ; but as the moon is carried 
by the earth around the sun, and as the moon's orbit in 
the course of an entire revolution of the earth is thus 
presented to the sun at opposite points of the orbit under 
reverse circumstances, there is a compensation accom- 
plished, so far as the angle of inclination is concerned, and 
also a partial compensation in the retrogression of the 
line of nodes of the moon's orbit, but not such as to pre- 
vent, in the end, a complete revolution of the moon's 
nodes in a period which we have already seen amounts to 
eighteen years and two hundred and nineteen days. 

We havo thus attempted to present a general account 
of the effect of a disturbing force. These same principles 
may bo extended yet further, and will give a general 
idea of the effeotS produced by the planets and their 
satellites upon each other. 



206 THE LAWS OF 

If we return for a moment to the hypothesis that the 
earth is the only planet revolving about the sun, the mag- 
nitude of its orbit, as well as the length and position of the 
line of apsides, will remain for ever fixed. If, however, we 
introduce into our system a new planet revolving in an 
orbit interior to that of the earth, whatever force is exerted 
upon the earth by the attractive power of this new planet 
will go to reinforce the power exerted by the sun ; and 
hence the disturbing influence of the planet will tend to 
diminish the magnitude of the earth's orbit, and to de- 
crease its periodic time. If the disturbing planet revolve in 
the same direction with the earth, by applying the reason- 
ing hitherto used we shall find that its effect will be to cause 
the perihelion point of the earth's orbit to advance and 
retreat during the revolution of the disturbing body, 
always leaving, however, a slight preponderance of the 
advancing movement over the retrograde. 

In case the disturbing body revolve in an orbit ex- 
terior to that of the earth, then its effect will be to ex- 
pand the earth's orbit and to increase the periodic time, 
while the influence exerted upon the position of the line 
of apsides will, in the long run, produce an advance. 

The reasoning hitherto employed with reference to the 
inclination of the moon's orbit to the ecliptic is directly 
applicable to the effect produced by any planet upon the 
inclination of the orbit of any other planet, as referred 
to a fixed plane. Take the earth for example, and let 
us consider the effect of any planet either interior or ex- 
terior upon the inclination of this plane to any fixed 
plane. So long as the disturbing body is revolving in 
that part of its orbit lying below the plane of the eclip- 
tic the tendency of the disturbing force will be to draw 
the earth from its undisturbed path below the plane of a 



MOTION AND GRAVITATION. 207 

fixed ecliptic, while this effect will be reversed whenever 
the disturbing planet shall pass through the plane of the 
ecliptic, and commence the description of that part of its 
orbit which lies above this plane. 

From the above reasoning it is clearly manifest that as 
not a solitary planet or satellite is moving undisturbed 
under the attractive power of its primary body, not one 
of the heavenly bodies describes rigorously an elliptic 
orbit, nor does the line joining the sun with any planet 
sweep over precisely equal areas in equal times, neither 
are the squares of the periodic times of the planets exactly 
proportioned to the cubes of their mean distances from the 
sun. In short, every law of Kepler, whereby perfect 
harmony seemed to be introduced among the heavenly 
bodies, is now seen to fail in consequence of the law of 
universal gravitation, and we find ourselves surrounded 
by a problem of wonderful grandeur, but of almost in- 
finite complexity. Before this problem can be fully 
solved we must measure the distance which separates 
every planet from the sun, and which divides every satel- 
lite from its primary ; we must weigh the sun and all his 
planets and every satellite ; we must determine the exact 
periods of revolution of each of these revolving worlds ; 
and when all this is accomplished, to trace out the re- 
ciprocal influences of each upon the other demands 
powers of reasoning far transcending the abilities of the 
most powerful genius, and hence the mind must either 
forego the resolution of this problem, or prepare for itself 
some mental machinery which shall give to thought and 
reason the same mechanical advantages which are ob- 
tained for the physical powers oi' the body by the in- 
vention and construction oi' the mighty engines of modern 
mechanics. 



208 THE LAWS OF 

This has actually been accomplished in the discovery 
and gradual perfection of a branch of mathematics called 
the infinitesimal analysis. "Up to the time of Newton, 
the mind employed alone the reasoning of geometry in 
the examination and discussion of the problems presented 
in the heavens. Even Newton himself was content to 
publish to the world the results of the application of the 
law of gravitation to the movement of the planets and 
their satellites under a geometrical form, exhibiting, in 
the use of these old methods, a sort of gigantic power 
which has ever remained as a monument of his wonder- 
ful ability. 

He was, however, fully conscious of the fact, that the 
mind demanded for its use ; in a full investigation of the 
physical universe — in the pursuit of these flying worlds, 
journeying through space amid such a crowd of disturb- 
ing influences — a far more subtle, pliable, and powerful 
mental machinery than that furnished in the cumbrous 
forms of geometrical reasoning. Conscious of this want, 
the genius of Newton supplied the deficiency, and gave 
to the world the infinitesimal analysis, which, as im- 
proved and extended by the successors of the great En- 
glish philosopher, has enabled man to accomplish results 
which seem to place him almost among the gods. 

The plan of our work does not permit any attempt to 
explain the nature and powers of this new method of 
reasoning. We can only illustrate imperfectly the differ- 
ence between the use of geometry and analysis. The 
demonstration of a problem by geometry demands that 
the mind shall comprehend and hold the first step in the 
train of reasoning, then, while the first is held, the second 
must be comprehended, and while intently holding these 
two steps, the third must be mastered and held, while 



MOTION AND GRAVITATION. 209 

the mind advances to the fourth step ; thus progressing 
with a constantly accumulating weight oppressing the at- 
tention, and tending to crush and destroy further effort 
to advance, till, finally, the steps become so numerous 
and complex that only those possessed of a genius of sur- 
passing vigor are able to reach in safety the last step, 
and thus grasp the full demonstration of the problem. 
Such is the reasoning of geometry. That of analysis is 
entirely different. Here the great effort is put forth to 
master fully and perfectly the conditions of the problem, 
and then to fasten upon the problem thus mastered the an- 
alytical machinery demanded in its resolution. This once 
accomplished, the mind puts forth its energy and accom- 
plishes the first step, and may there stop and rest, in the 
full confidence that what has been gained can never be 
lost. Days, even months may pass, before the problem 
be resumed, but in this lapse of time there is no loss, and 
the investigation may be taken up precisely where it was 
left off; and so one step after another may be taken, 
each dependent on the other, but each in some sense 
stereotyped as the mind advances, and remaining fixed 
without the putting forth of any mental effort to retain 
it. In short, geometry demands a vigor of mind suffici- 
ent to grasp, and hold at the same instant, every link in 
the longest and most complex chain of reasoning, while 
analysis only requires a power of genius sufficient to deal 
with individual links in succession ; thus, in the end, 
reaching the conclusion by short and comparatively easy 
mental marches. 



CHAPTER XI. 



INSTRUMENTAL ASTRONOMY. 



Method foe Obtaining tiie Mass of the Sun.— Foe Getting the Mass of a 
Planet with a Satellite. — Foe Weighing a Planet having no Satel- 
lite.— Foe Weighing the Satellites.— Planetaby Distances to be 
Measured. — Intervals between Primaries and their Satellites to be 
Obtained. — Intensity and Direction of the Impulsive Forces to be 
Determined.— These Problems all Demand Instrumental Measures. — 
Differential Places.— Absolute Places. — The Transit Instrument.— 
Adjustments.— Instrumental Errors.— Corrections Due to Various 
Causes.— American Method of Transits.— Meridian Circle.— The De- 
clinometer. 



The general reasoning presented in the preceding 
chapter can only be reduced to exact application after 
having obtained the numerical values of the quantities 
demanded in the investigation. The mathematician may 
assume these quantities at his pleasure, and with the as- 
sumed weight of his sun, and planets and satellites, and 
with their assumed distances, and with the assumed di- 
rections and intensities of the impulsive forces, he may 
master, by analytical reasoning, all the circumstances 
attending the revolutions of these supposed worlds, and 
thus trace their imaginary history for ages, either past or 
future. 

This is the work of the pure mathematician. The 
physical astronomer takes up the general mathematical 
reasoning thus perfected, and to employ it in writing out 



INSTRUMENTAL ASTRONOMY. 211 

the history of the real bodies constituting the solar sys- 
tem, lie must measure the actual distances between the 
sun and the planets, and the distances from each primary 
to its satellites ; lie must weigh exactly the sun and each 
of the planets and satellites, and he must measure in 
some way the direction and intensity of the impulsive 
forces by which the planets and their satellites were pro- 
jected in their respective orbits. 

We shall now proceed to show that the determination 
of all these quantities depends on exact astronomical 
measurements, which measurements demand the inven- 
tion and construction of instruments of the highest order 
of power, delicacy and perfection. 

To weigh the sun and planets. — Let it be borne in 
mind that the law of gravitation asserts that bodies at- 
tract with a force or power directly in proportion to their 
mass or weight. Hence a sun, weighing twice as much 
as the central orb of the solar system, would (at the 
same distance) attract with a double force. The same is 
true of the earth ; and if it were possible to hollow out 
the interior of the earth until its weight were reduced to 
one-half of what it is now, its power of attraction would 
be diminished in the same exact proportion. 

Thus, to know with what power the sun or any planet 
or any satellite attracts a body at a given distance, we are 
compelled to ascertain the exact weight of the sun, planet, 
or satellite. 

We shall show hereafter that it is possible to reach an 
approximate value of the weight of the earth in pounds 
avoirdupois, but for our present purpose it will be sufficient 
to state that the weight of the earth is well represented 
by the intensity of its power of attraction at a unit's dis- 
tance from its center. For this unit of length we will 



212 INSTRUMENTAL ASTRONOMY. 

take the earth's radius, and hence a body on the surface 
is attracted by a force or power such as will measure the 
mass or weight of the earth ; but the intensity of any 
force is measured by the quantity of motion it is capable 
of generating in a given time. Hence the intensity 
of the earth's attractive power will be correctly meas- 
ured by the velocity it impresses on a body free to 
fall, in, say, one second of time. This is a matter of the 
simplest experiment, by which it is found that the earth's 
attractive power generates in one second a motion in a 
falling body such as to carry it over a space equal to 
about sixteen feet in one second. In case the earth were 
twice as heavy, the space passed over by a falling body in 
one second would be doubled, and so forward in like pro- 
portion for any increase of weight. 

Having thus found a measure of the weight of the earth 
in the space passed over in a second of time by a falling 
body, in case it were possible to transport this body to 
the surface of the planet Venus (assuming the diameter 
of Venus and the earth to be equal), then permitting it to 
fall, and measuring the space over which it passes in one 
second, this space would hold the same proportion to six- 
teen feet as the weight of Venus does to that of the earth. 
If the diameters of the planets are unequal, then we 
must take into account the fact that the falling body is 
not at equal distances from the centers of the planets, 
and that the force of attraction is thus diminished in- 
versely as the square of the distance from the center is 
increased. Let us attempt to weigh two planets whose 
diameters are in the proportion of one to two. At the sur- 
face of the smaller planet suppose the body falls sixteen feet 
in one second, while at the surface of the larger planet it 
passes over sixty-four feet in the same time. In case the 



INSTRUMENTAL ASTRONOMY. 213 

diameters were equal this result would show that one 
body was four times as heavy as the other ; but the fall- 
ing body is twice as far from the center of the large 
planet as it is from the center of the small one, and hence 
the force or power of attraction of the large planet is 
only one-fourth part what it would have been in case the 
falling body had been brought to within one unit of its 
center. If, then, with an energy reduced at a distance 
of two units to one quarter, it causes a fall of sixty-four 
feet in one second, the entire energy would, at a unit's 
distance, cause a fall through four times sixty-four feet, 
or through 256 feet, and hence the weights of the plan- 
ets under examination are in the proportion of 16 to 
256 or 1 to 16. 

The train of reasoning here presented may be extended 
to embrace any given case, and if it were possible to 
make the experiment of the falling body, as above de- 
scribed, at the surfaces of the sun, planets and satellites, 
(admitting that we know the diameters of all these bodies,) 
then would it be possible to ascertain their masses, as 
compared with that of the earth, taken as a unit. 

But it is impossible to pass to the sun and planets for 
such experimentation, and hence we must devise some 
substitute which may fall within the limits of practicabil- 
ity. To obtain the relative weights of the sun and earth 
we have only to call to mind the fact that the moon, un- 
der the power of the earth's attraction, is ever falling 
away from the rectilineal path in which it would ily 
but for this very power of attraction, while in like 
manner the earth is ever falling away from the right 
line in which it would move but for the attractive 
energy of the sun. Here, then, are two bodies, the 
earth tailing to the sun, the moon tailing to the earth ; 



214 INSTRUMENTAL ASTRONOMY. 

and in case we could measure the precise distance which 
each of these bodies falls, under the respective powers of 
attraction exerted on them, taking into account the effect 
produced on the two forces by the inequality of the dis- 
tances at which they operate, we should reach the exact 
relative weights of the sun and earth. Thus, admitting 
that the distance at which the sun operates on the earth 
is 400 times greater than the distance at which the earth 
operates on the moon, in case the effects were equal the 
sun would be 160,000 times heavier than the earth, since 
its power of attraction is reduced by the distance in this 
exact ratio. But again, admitting that we find, even 
with this high reduction, the sun's power on the earth is 
still two and a half times greater than the earth's power 
on the moon, (as is shown in their respective deflections 
from a right line in one second of time,) then will the 
sun be 2^x160,000 times heavier than the earth, and 
this, indeed, as we shall find hereafter, is about the re- 
lative weights of these two globes. 

To resolve this great problem, then, of weighing the 
sun against the earth, we must first measure the sun's 
distance and the moon's distance, and the exact amounts 
by which the earth and moon are caused to fall away 
from a rectilineal orbit in one second of time, which meas- 
urements demand instruments of the highest order. 

TO WEIGH AGAINST THE EARTH, A PLANET ATTENDED 

BY A satellite. — In case any planet be attended by a 
satellite, if we can measure the precise distance separat- 
ing these two bodies, and determine the period of revolu- 
tion of the satellite, we can thence derive the weight of 
the planet as compared with that of the earth. To fix 
our ideas, let us suppose Jupiter's nearest satellite to be 
as far from Jupiter as our moon is from the earth, and to 



INSTRUMENTAL ASTRONOMY. 215 

perform its orbital revolution in the same exact time oc- 
cupied by the moon. This would prove Jupiter to be 
just as heavy as the earth. But suppose now that at 
equal distances Jupiter's moon revolves ten times as 
rapidly as the earth's moon, this fact proves that Jupiter 
must be one hundered times as heavy as the earth. This 
is evident from what we have already said, that the 
centrifugal force in any revolving body increases as the 
square of the velocity ; and as the moon of Jupiter is 
now supposed to revolve ten times as fast as our moon 
its centrifugal force will be one hundred times as great 
as that of the earth's moon ; and hence Jupiter's attrac- 
tion to counterbalance this tendency to fly from the cen- 
ter must be one hundred fold greater than that of the 
earth. This is on the hypothesis of equal distances. 
But if Jupiter's moon be supposed to be twice as remote 
from its primary, and to revolve ten times as rapid as 
our moon, then will it be demonstrated that Jupiter is 
one hundred times heavier, on account of the square of 
the velocity of the revolving moon, but this weight must 
be multiplied by the square of two on account of the 
double distance at which it acts. Hence, under these 
circumstances Jupiter would be 400 times as heavy as 
the earth. 

Thus, to determine the weight of a planet in terms of 
the earth's weight as unity, we must learn the exact dis- 
tance and periodic time of our moon, and also the interval 
by which the planet and its moon are separated, avS well 
as the period of revolution of the satellite, all of which 
again demand the use of instruments of a high order of 
accuracy and delicacy. 

TO WEIGH A PLANET HAVING NO SATELLITE. — Tluve 

of the planets, viz. : Mercury, Venus, and Mars, so 



216 INSTRUMENTAL ASTRONOMY. 

far as known, are not accompanied by a moon. The 
preceding method of obtaining the mass or weight will 
not apply to either of these planets. It is only after 
acquiring a very exact knowledge of the movements of 
•the planets whose masses may be derived from their satel- 
lites that it becomes possible to determine the weights of 
the remaining planets. Let us suppose that the earth 
alone revolved around the sun, and that its orbit was 
perfectly determined. In an exterior orbit of known 
dimensions let us place the planet Mars. This will at 
once modify the former orbit of the earth, and the change 
will depend, in quantity, upon the mass of the new planet ; 
and in case it became possible to measure these changes, 
their values will give the weight of the body producing 
them. 

The same hypothesis remaining with reference to the 
earth's orbit, we may imagine the new planet to revolve 
in the orbit of Venus, interior to that of the earth, and 
the same kind of investigation will lead to the determina- 
tion of the mass of this interior planet. 

We shall see hereafter that certain periodical comets, 
favorably located, furnish the means of corroborating the 
results reached by the above train of reasoning, by the 
data their perturbations furnish for reaching the mass of 
the planet producing these effects. 

To weigh the satellites. — The effect produced by 
the moon on the earth in causing the figure of its orbit 
to sway to and fro under the moon's attractive power 
furnishes again the data whereby the moon's mass may 
be determined. In the case of many satellites to the 
same planet, their effects on each other being carefully 
determined, furnish the means of computing their masses. 
This, however, is a difficult problem, and one in which a 



INSTRUMENTAL ASTRONOMY. 217 

solution has been effected only in the system of Jupiter. 
The masses of the satellites of the other superior planets 
have as yet not been obtained with any reliable cer- 
tainty. 

We have thus presented methods by which the masses 
of the sun, planets and satellites may be obtained, pro- 
vided certain measurements can be made, which measure- 
ments demand the aid of powerful ; and accurate instru- 
ments. 

The distances separating the sun and planets, and 
separating the primaries and their satellites, must be 
obtained before we can trace the history of any one of 
these revolving worlds. We have already explained the 
processes by which the earth's distance from the sun may 
be obtained by the use of the phenomena attending the 
transit of Venus. This problem again demanded instru- 
mental measurement. Admitting the earth's distance 
from the sun to be known, Kepler's third law will give 
the distances of all the planets of our system, provided 
we have obtained their periods of revolution around the 
sun. The method of obtaining the periodic times has 
also been explained, and in this process instrumental 
measurements are demanded. 

In like manner, to reach the periods and distances 
of the satellites, their elongations, occultations and 
eclipses, must bo carefully measured and noted, demand- 
ing instruments of a high order. 

To trace a planet or satellite, in addition to the quan- 
tities already pointed out, wo have seen that we must 
know the intensity of the impulsive force by which it 
was projected in its orbit. But we have Been that the 
intensity of any impulse is measured by the velocity it is 
capable of producing in a unit oi* time. Admitting, 



218 INSTRUMENTAL ASTRONOMY. 

then, that we know the distance of a planet from the 
sun, and its period of revolution, we know the velocity 
with which it moves, in case its orbit be circular. The 
earth, for example, in 365} days accomplishes a jour- 
ney round the sun in a circle whose diameter is 
190.000,000, and whose circumference is equal to this 
quantity taken 3.14156 times. Hence, by dividing the 
number of miles traveled in the entire circuit by the 
number of days occupied in the journey, we have the rate 
per diem, or velocity. Dividing the space passed over 
in one day by 24, we have the rate per hour, and finally 
may obtain the rate per second. If the orbit be not 
circular, we can always find a circle which, for a very 
short distance, will coincide with an elliptic or other 
curve, and on this circle we may suppose the planet to 
move for a very short time, as one second, with uniform 
velocity, and the space passed over in this unit will 
again measure the intensity of the impulsive force at this 
part of the orbit. Here again we have presupposed a 
knowledge of the magnitude and figure of the elliptic 
orbit before the intensity of the impulsive force can be 
reached, and to determine these quantities instrumental 
measurement is demanded, requiring instruments of great 
perfection. 

The last quantity demanded by the mathematician in 
writing out the history of a planet moving in space is 
the direction of the impulsive force projecting it in its 
orbit. This is readily obtained when we shall have 
learned the exact direction of a line tangent to any point 
of the planetary orbit ; for the direction of the impulse 
must always be tangent to the curve described by the 
body set in motion. If we join the planet with the sun 
by a right line, this line will form an angle with tangent 



INSTRUMENTAL ASTRONOMY. 219 

to the planetary orbit; and we shall find hereafter that 
the nature of the orbit will depend upon the value of this 
angle, or in other language, on the direction in which 
the impulse is applied. 

Thus we find that not a single quantity of the five 
required to determine the circumstances of motion of a 
body revolving under the laws of motion and gravitation 
can be reached without instrumental measurement ; so 
that our entire knowledge of the physical universe hangs 
at last on the accuracy and perfection of the instruments 
which have been invented and constructed for making 
these measures, a fact which elevates instrumental as- 
tronomy to a position of the highest dignity and im- 
portance. 

The measures demanded in instrumental astronomy are 
divided into two great classes. In thejirst class all the 
measures of position are absolute, that is, a star or planet 
whose place is thus determined is located on the celes- 
tial sphere, and fixed for the moment in position by a 
measure of its distance, say, from the north pole of the 
heavens along the arc of a great circle, and also its dis- 
tance measured on the equinoctial from the vernal equi- 
nox, or from some other fixed points which may have 
been selected. In the second class all the measures aro 
relative or differential ; that is, an interval between two 
points in close proximity is determined. To this class 
belong the measures of the diameters of the sun and 
moon and planets; the elongations of the satellites from 
their primaries ; tho measures of the transits of Venus 
and Mercury across the disk of the sun ; the measures of 
the solar and lunar spots ; the distances between tho 
double and multiple stars ; in short, all those measures 
involving mere differences of position. 



220 INSTRUMENTAL ASTRONOMY. 

Each of these classes of measures demands its own 
peculiar and appropriate instruments, each of them in- 
volving the data required in the solution of the sublimest 
problems of celestial science. 

We shall now proceed to exhibit an outline of the 
structure of a few of the most important instruments be- 
longing to these two classes, only for the purpose of pre- 
senting the extraordinary difficulties which must be 
met and conquered in the seemingly simple mechanical 
problem of fixing the place of a star in the celestial 
sphere. 

For the purpose of giving position to the heavenly 
bodies astronomers refer them to the surface of a celes- 
tial sphere, whose poles are the points in which the 
earth's axis prolonged pierces the sphere of the fixed 
stars. To determine a point on the surface of any 
sphere we must fix its distance on the arc of a great 
circle from the north pole, and we must also know the 
distance of the meridian line on which it is located, from 
a fixed meridian. 

Astronomers have chosen for their prime meridian that 
one which passes through the vernal equinox, and as the 
celestial sphere revolves to our senses with uniform velo- 
city once in twenty-four hours, the vernal equinox will 
come at the end of this period to the meridian of the 
place from whence it started. Any object, therefore, 
which crosses the meridian of a given place an hour 
later than the vernal equinox has its place fixed some- 
where on the circumference of a known meridian, or 
hour circle. If at the same time its distance from the 
north pole can be determined, its position on the celes- 
tial sphere will be positively defined by these two ele- 
ments. As we have already seen, the vernal equinox is 



INSTRUMENTAL ASTRONOMY. 221 

the point in which the great circle of the heavens, cut 
out by the indefinite extension of the plane of the earth's 
orbit, intersects the equinoctial circle, or that circle cut 
from the celestial sphere by the indefinite extension of 
the plane of the earth's equator. If the vernal equinox 
were absolutely fixed, and if in that point a star were lo- 
cated, this star would revolve with all the other stars of 
the heavens once in twenty-four sidereal hours. To 
mark the movement of this vernal equinox astronomers 
employ the sidereal clock, whose dial is divided into 
twenty-four hours, and which, when perfectly adjusted, 
will mark Oh. Om. Os. at the moment the vernal equinox 
is on the meridian of the place where the clock is located. 
All points on the celestial sphere will, pass the meridian 
necessarily at intervals of time marking the position of 
the hour circle in which they are located, relative to the 
prime meridian passing through the vernal equinox. 
These intervals of time which elapse between the passage 
of the vernal equinox across the meridian of a given place, 
and the passage of any heavenly body across the same 
meridian, are called right ascensions. Thus a star 
which follows the vernal equinox, after an interval of 
2h. 10m. 20s., as marked by a perfect sidereal clock, has 
a right ascension of 2h. 10m. 20s. 

Thus, to fix the place of any heavenly body on the 
celestial sphere, two instruments have been devised, the 
one having for its object to measure north polar dis- 
tances, while the other is employed in the measurement 
of right ascensions ; the first of these is denominated a 
mural circle, while the second is called a transit in- 
strument. 

We shall first consider the principles involved in the 
construction of the transit instrument. This instrument 



222 INSTRUMENTAL ASTRONOMY. 

consists of a telescope mounted upon an axis perpendicu- 
lar to the axis of the tube of the telescope. This per- 
pendicular axis terminates at each extremity in two 
pivots of equal size and perfectly cylindrical in form. 
To give support to this instrument a solid pier of masonry 
is built, resting upon a firm foundation, and isolated from 
the surrounding building. On the upper surface of this 
stone pier two stone columns are placed, whose centers 
are separated by a distance equal to the length of the 
axis of the transit ; on the tops of these columns metallic 
plates are fastened, to which metal pieces are attached, 
cut into the shape of the letter Y. If in these Y's the 
pivots of the transit be laid, in case the axis be precisely 
level, and lying due east and west, then the axis of the 
telescope, or visual ray, being carried around the heavens, 
by revolving the instrument in its Y's, will describe a 
meridian line which will pass through the north pole of 
the heavens. If this meridian line could be rendered 
visible it would be possible to note the passage of any 
star or other heavenly body across this visible meridian. 
This cannot be accomplished directly, but the same end 
is reached by stretching a delicate filament of spider's 
web across the center of a metallic ring, and placing it in 
the focus of the eye-piece of the telescope; when this 
spider's web is lighted up by a lamp, through a suitable 
orifice, it is seen as a delicate golden line of light stretch- 
ing across the field of view, and resting on the dark back- 
ground of the heavens. E evolving the ring which bears 
the spider's web, we may bring this web to coincide, 
throughout its entire length, with a true meridian line, 
and thus, in reality, we procure for ourselves a visible 
meridian quite as perfect for our purposes as though it 
were an actual line of light, sweeping from north to south 



INSTRUMENTAL ASTRONOMY. 223 

across the celestial sphere. To render visible the axis 
of the telescope, or to direct the visual ray, another 
spider's web is stretched across the field of view, in di- 
rection perpendicular to the first, and precisely in the 
center of the field, so that by their intersection these 
spiders' webs form a point of almost mathematical mi- 
nuteness. 

Let us now examine what is demanded in the construc- 
tion of the transit to render it an instrument perfect in 
performance. The object-glass and the eye-piece, form- 
ing the optical portion of the telescope, should be per- 
fect in their figure and adjustments ; the tube in which 
they are placed should be perfectly rigid and inflexible ; 
the optical axis or line of collimalion should be exactly 
perpendicular to the horizontal axis on which the instru- 
ment revolves ; the pivots should be exactly equal to 
each other, and precisely cylindrical in form ; the hori- 
zontal axis should lay in a direction exactly east and 
west, and should be absolutely level. In connection with 
the transit we require a perfect time-keeper. The clock, 
when properly adjusted, will mark Oh. 00m. 00s. at the 
moment the vernal equinox is seen to pass the visible 
spider's line meridian of the telescope ; it must then 
move uniformly during the entire revolution of the heav- 
ens, and mark the zero of time again when the vernal 
equinox returns to the meridian line. Such are the me- 
chanical demands required in the construction and use of 
the transit and clock ; but to obtain a perfect result the 
observer is required to perform his part in the operation ; 
he must note the exact ins/ant at which the vernal equi- 
nox passes the visible meridian, so as to set his sidereal 
clock; this being accomplished, to obtain the right ascen- 
sion of any heavenly body he must seize the precise mo- 



224 INSTRUMENTAL ASTRONOMY. 

merit, as marked by his clock, at which the center of the 
object under observation passes the meridian. 

To obtain, then, the element of right ascension, required 
to fix the place of a heavenly body at a given moment, we 
require a perfect transit, perfectly adjusted, a perfect 
clock, perfectly rated, and a perfect observer, with a per- 
fect method of subdividing time into minute fractions. 
Not one single one of these demands can ever be met. 
Even admitting the possible construction of a perfect in- 
strument, every change of temperature will effect certain 
changes, in the material of which it is composed. No 
two pivots can possibly be made exactly equal, nor pre- 
cisely cylindrical in form ; and should the observer suc- 
ceed in placing the axis of his transit so as to lie east 
and west, as well as horizontal, it will not remain in this 
position for even a single hour of time. If the clock be 
adjusted so as to mark the exact zero of time, and to 
move off with a uniform rate, this rate will soon sensibly 
change, and must be carefully watched even from hour 
to hour. The observer himself is but an imperfect and 
variable machine, utterly incapable of marking the exact 
moments required, his work being subject to errors, 
whose values fluctuate from day to day ; and to add to 
all these difficulties, the atmosphere which surrounds the 
earth not only possesses the power of diverting the rays 
of light from their rectilineal path, but because of its con- 
stant fluctuations and changes produces a tremulous or 
dancing motion in the stars under observation which, to 
a certain extent, renders it impossible to do exact work, 
even with perfect instruments and perfect observers, could 
such be found. 

We will now examine the instrumental means required 
to determine the second element, the north polar dis- 



INSTRUMENTAL ASTRONOMY. 225 

tance, which is demanded in fixing the place of a 
heavenly body. For this purpose let us suppose a metal- 
lic circle to be permanently fastened to the horizontal 
axis of the transit, having its center in the central line 
of the axis, and its plane perpendicular to this line. Let 
us suppose the rim of this circle to be divided into de- 
grees, minutes and seconds of arc, and this division to 
have been perfectly accomplished. Let us direct the 
transit telescope precisely to the north pole of the 
heavens, and when thus directed let us fix upon the stone 
pier a permanent mark or pointer, directed to the zero 
point on the divided circle. As we turn the transit away 
from the north pole toward the south the zero point on 
the circle will in like manner leave the fixed pointer, and 
thus the distance from the north pole to any object to 
which the telescope may be directed will be read on the 
divided circle from the zero round to the division to 
which the pointer directs. Such an instrument is called 
a meridian circle. Here again new mechanical diffi- 
culties present themselves. The centering of the circle., 
the perfection of the divisions upon its circumference, are 
matters which cannot be accomplished with absolute ac- 
curacy ; and even if this were possible, they arc liable to 
changes to which all material is subjected at every mo- 
ment. The same is true of the stability of the pointer, 
any change in whose position must involve an error in 
the measured north polar distance. 

Thus far we have supposed that in our celestial sphere 
we have two fixed points of reference, namely, the ver- 
nal equinox and the north polar point. Unfortunately 
for the observer, and to increase the difficulties by which 
he is surrounded, neither o( these points remains abso- 
lutely fixed, and even their rate of movement is not uni- 
10* 



226 INSTRUMENTAL ASTRONOMY. 

form ; and tbus one difficulty rises above another, cul- 
minating in the fact that even the light whereby objects 
become visible does not dart through space with infinite 
velocity, but wings its flight with a measurable speed, 
which, when conjoined with the speed of the earth's re- 
volution in its orbit, sensibly changes the apparent place 
of every object under examination. Add to this long 
catalogue of difficulties the fact that the earth's rotation on 
its axis is rapidly revolving the observer, his instruments 
and observatory, at a possible rate of a thousand miles an 
hour, and some idea may be formed of the embarrassments 
under which astronomers are compelled to work out the 
resolution of the great problems of the heavens. 

Having presented this array of difficulties, we shall 
not undertake to show in every instance by what precise 
means they are overcome. So far as regards the move- 
ment of the vernal equinox and the north pole, the most 
extended and elaborate observations have been made 
through a long series of years by the best instruments 
and the most skillful observers, and these have been re- 
duced and discussed by the most able mathematicians, 
until by different methods astronomers have reached to so 
perfect a knowledge of the values of the errors due to 
these two causes that it seems as though no greater ap- 
proximation to accuracy can be made by the same methods. 
That correction due to the movement of the vernal equi- 
nox is called precession ; that due to the movement of the 
north pole is called nutation, of which we shall give a 
more accurate account hereafter. The error arising from 
the velocity of light, combined with the orbital and ro- 
tary motion of the earth, is called aberration. This 
subject will also be treated hereafter. Of the three 
principal instrumental errors, that arising from want of 



INSTRUMENTAL ASTRONOMY. 227 

exact perpendicularity in the position of the axis of the 
telescope to the horizontal axis of the transit is called the 
coUimation error, and may be detected and measured by 
mechanical means ; its effect is to cause the visual ray to 
pierce the heavens east or west of the true meridian, and 
in the revolution of the transit this point of piercing will 
describe a small circle of the sphere, instead of the great 
meridian circle, which it ought to describe. The error 
arising from a failure to place the transit axis in a truly 
horizontal position is called the level error ; its effect is 
to cause the visual ray to pierce the heavens east or west 
of the true meridian, and the point of piercing, by 
the revolution of the transit on its axis, will describe 
a great circle of a sphere inclined to the true meridian, 
under an angle equal to that which the axis of the tran- 
sit makes with the horizon, or equal to the level error. 
The failure to place the axis of the transit precisely 
east and west gives rise to what is called the azimuthal 
error. This causes the visual ray or line of collimation 
of the telescope to pierce the heavens on the true meri- 
dian only when directed to the zenith. This point of 
piercing, by revolving the transit on its axis, describes a 
great circle, which departs from the true meridian at the 
zenith, under an angle precisely equal to the azimuthal 
error. Methods have been devised for measuring these 
various errors, and for computing their effect upon the 
apparent places of the heavenly bodies. 

The rays of light by which every object is rendered 
visible, as we have already stated, on entering the earth's 
atmosphere are bent from their rectilineal path, giving 
rise to a source of error called infraction. The laws 
governing the direction of the light, as affected by the 
atmosphere, have been carefully studied, so that at 



228 INSTRUMENTAL ASTRONOMY. 

present it is possible to compute with great exactitude 
the change of place of any object under observation due 
to the effects of refraction. The flexure of the tube of 
the telescope, under the various circumstances by which 
it may be surrounded, have been thoroughly investigated, 
while the exact figure of the pivots of the axis has been 
subjected to the most rigorous mechanical tests ; in short, 
all the mechanical deficiencies in the instrument have 
occupied the attention of many of the best minds for the 
past two hundred years, and thus slow but steady ad- 
vances in accuracy have been accomplished. 

To remedy the errors arising from the perturbations of 
the atmosphere, as well as those arising from personal 
error in the observer, in seizing the moment of transit 
across the visible meridian line, several spider's lines, 
commonly called wires, parallel to each other, have been 
introduced into the focus of the eye-piece of the transit, 
and thus the instant at which the star passes each one 
of these wires being noted as accurately as possible, the 
average of all gives a better result than could have been 
obtained from any one wire. 

To remedy the defects arising from the imperfect 
divisions, from imperfect centering, and from changes of 
figure in the circle from whence the north polar dis- 
tances are read, it is usual to have four pointers, and 
even sometimes six, by means of which the north polar 
distance is read in as many places on the divided circle, 
the average of all giving a better result than any one 
reading. These pointers, as we have named them, are in 
raality powerful microscopes, permanently fixed in the 
heavy stone pier, on which the instrument rests, and 
having their visual ray fixed by the intersection of 
spiders' webs, as in the principal telescope. 



INSTRUMENTAL ASTRONOMY. 229 

From these instrumental imperfections we pass to those 
which belong to the clock, and here again we are com- 
pelled to work with an imperfect machine. No clock has 
ever been made which can keep perfect time, and the 
great object of the observer is to learn the peculiarities 
of his clock, to determine its deviations from absolute 
accuracy, and to be able to mark these deviations, if pos- 
sible, from minute to minute. 

The observer, having mastered all the sources of error 
above described, next comes to the consideration of his 
own personal deviations from accuracy in attempting to 
mark the moment at which a star crosses his visible me- 
ridian. To observe the transit of a star across the meri- 
dian, he places himself at the transit instrument, enters in 
his note-book the hour and minute from the face of the clock, 
then fixing his eye through the telescope upon the star, 
and counting the beats of the pendulum, he follows the 
star as it slowly advances to the meridian wire. Between 
some two beats thus counted the star crosses the wire. 
The observer holds in his mind, as well as he can, the 
star's position at the close of the beat before the passage, 
and at the close of the next beat after the passage, and 
mentally subdividing this space passed over in one second 
into ten equal parts, he estimates how many of these 
parts precede the passage of the star across the meri- 
dian, and these parts are the fractions or tenths of a 
second, which mark the time of transit. Thus he adds 
to the entry in his note-book already made the number 
of beats of the pendulum and also the fractions oi' a 
second above obtained, and thus the time of transit is 
obtained, approximately to the tenth part of one second 
of time. 

In the method of observing transits just explained so 



230 INSTRUMENTAL ASTRONOMY. 

many things are demanded of the observer that his atten- 
tion cannot be given exclusively to the determination of 
the moment of transit ; he must keep up the count of the 
clock beat ; he must hold in his mind the interval passed 
over by the star from one beat to the next during the 
transit ; he must divide this space by estimation into 
tenths ; he must assign the number of tenths which pre- 
cede the transit ; he must enter the seconds and tenths in 
his note-book, keeping up the count of the beats of the 
pendulum, and thus pass from one wire to the next suc- 
cessively through all the system of wires, so that in this 
multiform effort his powers of attention are taxed beyond 
what they are able to bear, and it is only by long prac- 
tice that any valuable results are ever reached. The ob- 
server also finds that his modes of observation often lead 
him into false habits. He may mark the time from his 
own mental count of the beat, rather than from the 
sound of the beat itself, or he may find himself running 
into the habit of fixing his tenths of seconds predominantly 
in one or two portions of the scale of tenths. It is 
manifest that in a thousand observations the tenth of a 
second on which the transit falls ought to be uniformly 
divided among the whole number. Thus there should be 
a hundred observations in which the time of transit 
should fall on the first tenth of a second, a hundred ob- 
servations in which the time should fall on the second 
tenth, and so on for each of the tenths. But an observer 
may find when he comes to examine a thousand of his ob- 
servations that two or three hundred are entered as fall- 
ing on the third tenth, and three or four hundred as 
falling on the seventh tenth. This only demonstrates 
that he has fallen into habitual error, due to the fact 
that he is compelled to estimate. In attempting to 



INSTRUMENTAL ASTRONOMY. 231 

escape from this particular error, and finding himself too 
much attached to one portion of his scale of tenths, he is 
very likely to fall into the other extreme, and thus he 
finds himself a variable instrument, always imperfect, 
even in these legitimate sources of error. 

By studying his own peculiarities more rigorously, and 
comparing himself with others, it will be found that in 
case the two persons compared could at the same time 
look through the same telescope at the same star coming 
up to cross the same meridian wire, each attempting to 
note the moment of passage, by listening to the beat of 
the same clock, the recorded times would differ, one of 
the observers being uniformly in advance of the other. 
Should this experiment be repeated, at the end of a 
month, with every possible precaution, the difference be- 
tween the two observers will in general be found to 
chano-e, demonstrating that one or the other or both have 
varied in this particular, and that an inter-comparison 
of their observations now made by the former difference 
would produce inaccurate results. This difference is what 
is denominated technically personal equation, and is sup- 
posed to arise from the fact that time is really an ele- 
ment in the operation of the senses : that two persons 
listening to the same sound, as the sharp crack of a pis- 
tol, the sense of hearing of the one may perform its office 
of conveying this sound to the brain more rapidly than 
the other, and that the same may be asserted of the sense 
of sight. 

For the purpose of comparing the observations of dif- 
ferent astronomers, it becomes necessary to determine the 
peculiarities of each, and it would be a matter of great 
importance if it were possible to fix some absolute stand- 
ard to which all observations might be reduced. This is 



232 INSTRUMENTAL ASTRONOMY. 

accomplished, so far as the three instrumental errors and 
the clock error are concerned, by actually applying a cor- 
rection which reduces each observation to what it would 
have been in case none of these errors had existed. The 
same may be said of the correction applied for refraction 
and for aberration. As to precession, the position of the 
equinoctial point, supposing it to move with its mean or 
average velocity, is always given for the epoch to which 
the observation is referred. The observations are also 
reduced for parallax whenever this element becomes 
sensible, and are thus recorded as though the observer 
were located at the center of the earth. To accomplish 
the inter-comparison of observations made at different ob- 
servatories, there yet remains the reduction due to differ*- 
ence of longitude, and that depending upon the personal 
peculiarities of the observers. 

The high demand for accuracy in instrumental obser- 
vation can only be fully appreciated by those actually 
engaged in the computation of the places of the heavenly 
bodies. Observations are valuable in the ratio of the 
squares of their probable errors : that is, if one set of 
observations can be produced in which the probable 
errors remain among the tenths of seconds of time, while 
in another set of observations the errors are driven into 
the hundredths of seconds, or are but one tenth part as 
large as the former, then the second set will be a hundred 
fold more valuable than the first. This principle applies 
to all observations, but there are some distances so great 
and some motions so slow that even the best and most 
delicate methods of observation hitherto applied fail alto- 
gether to measure the one or to appreciate the other. 
This remark is especially true when applied to the 
distance and movements which are found in the region 



INSTRUMENTAL ASTRONOMY. 233 

of the fixed stars. Among these remote objects, while 
in some instances the motion is sufficiently rapid to be 
detected and approximately measured, even in a single 
year, in other instances, and by far the larger number, 
these motions are so slow that they must accumulate for 
hundreds of years to become appreciable and measurable 
by the most refined and perfect instruments hitherto pre- 
pared by human skill. 

In the three great departments of astronomy there is 
but one in which there is much hope for increased facility 
and accuracy. The great laws of motion and gravitation 
are no doubt perfectly determined. The mathematical 
formulae whereby these laws are applied to the circum- 
stances of motion of the planets and their satellites are 
now brought to great simplicity and perfection ; and if it 
were possible to give to the physical astronomer perfect 
data, he would be able to obtain perfect results. We 
know by geometry that the area of a rectangle is the pro- 
duct of its base by its altitude. This rule or formula is ab- 
solutely accurate, and whenever we wish to apply it to de- 
termine the area of any particular rectangle we must first 
accomplish the mechanical measurement of the length of 
the base and altitude. To do this perfectly is impos- 
sible, but approximate results may be reached of greater 
or less precision in proportion to the accuracy of the in- 
struments employed, and the time and pains expended 
upon the work. Thus one measure may reduce the pro- 
bable errors to one hundredth of an inch, while in another 
the error may only reach one thousandth of the same 
unit. 

In like manner the theory and formula: of physical as- 
tronomy arc nearly, if not quite perfect, while, however, 
the observations whence we derive the data, to be used in 



234 INSTRUMENTAL ASTRONOMY. 

computation are, as we have seen, comparatively imper- 
fect. The author of this work has attempted to contri- 
bute something to the accuracy and facility of astronomi- 
cal observation. 

The following is a brief account of the circumstances 
attending the invention of this new mode of observation, 
now known as 

The American method of transits. — In the autumn 
of the year 1848, the late Professor S. C. Walker, then 
of the United States Coast Survey, was engaged with 
me at the Cincinnati Observatory in a series of observa- 
tions, having for their object the determination of the 
difference of longitude between the observatories of Phila- 
delphia and Cincinnati. In comparing our clocks or 
chronometers with those of Philadelphia, an observer at 
Philadelphia listening to the clock-beat touched the mag- 
netic key of the telegraph wire at every beat, and we re- 
ceived at Cincinnati an audible tick every second of 
time, which was carefully noted, and thus our clocks 
were compared. There were two sources of error in this 
method of comparison, arising from an imperfect imita- 
tion of the clock- beat by the Philadelphia operator, also 
from our noting the arrival of that beat in Cincinnati. 
On the 26th of October, 1848, Professor Walker, while 
conversing on this subject, first presented to me the me- 
chanical problem of causing the clock to send its own 
beats by telegraph from one station to the other, or 
what amounted to the same thing, the problem of convert- 
ing time into space, as already explained ; for in case 
the clock could send its own beats by telegraph, and 
these beats could be received on a uniformly flowing time 
scale, the star transit could be also sent by telegraph, and 
received on the same scale ; and thus a new method of 



INSTRUMENTAL ASTRONOMY. 235 

transits would at once spring from the resolution of the 
first mechanical problem. I was informed by Professor 
Walker that the problem had already been presented to 
others, but, so far as he knew, had never been solved. 
The full value of the idea was at once appreciated ; and 
on the same evening a common brass clock, the only 
one then in the observatory, was made to record its own 
beats by the use of the electro-magnet on a Morse fillet. 

The problem once solved, nothing more remained than 
to elaborate such machinery as would render it possible 
to apply this new discovery or invention to the delicate 
and positive demands of astronomical observations. 

It is well known that signals are transmitted along a 
line of telegraphic wire by closing or by breaking the wire 
circuit over which the electricity passes from pole to pole 
of the battery. The finger of the telegraphic operator, by 
touching a magnetic key, " breaks or makes " the circuit, 
and thus either interrupts or starts the flow of electricity. 
The problem of causing a clock to record its beats tele- 
graphically was then nothing more than to contrive some 
method whereby the clock might be made (by the use of 
some portion of its own machinery) to take the place of the 
finger of the living, intelligent operator, and " make" or 
" break" the electric circuit. The grand difficulty did not 
lie in causing the clock to play the part of an automaton in 
this precise particular, but it did lie in causing the clock to 
act automatically, and at the same time perform perfectly 
its great function of a time-keeper. This became a mat- 
ter of great difficulty and delicacy ; for to tax any por- 
tion of the clock machinery with a duty beyond the ordi- 
nary and contemplated demands of the maker, seemed 
at once to involve the machine in imperfect and irregular 
action. After due reflection it was decided to apply to 



236 INSTRUMENTAL ASTRONOMY. 

the pendulum for a minute amount of power, whereby the 
making or breaking the electric circuit might be accom- 
plished with the greatest chance of escaping any injurious 
effect on the going of the clock. The principle which 
guided in this selection was, that we ought to go to the 
prime mover (which in this case was the clock weights, 
and which could not be employed,) and failing to reach 
the prime mover, we should select the nearest piece of 
mechanism to it, which in the clock is the pendulum. 
A second point early determined by experiment and re- 
flection was this : that the making or breaking of the cir- 
cuit must be accomplished by the use of mercury, and 
not by a solid metallic connection. The method evolved 
and based on these two principles is the one which has 
been in use now for more than ten years in the Cincin- 
nati Observatory. 

The simplest possible method of causing the pendulum 
to " make " the circuit may be described as follows : 

Attach to the under surface of the clock pendulum 

with gum shellac a small bit of wire bent thus, , * 

then right and left of the point over which the pendu- 
lum vibrates when lowest place two small globules of 
mercury, into each of which there shall dip a wire from 
the poles of the battery. Now, as the pendulum swings 
over the globules of mercury, the two points of the at- 
tached wire will finally come, for one moment, to dip in 
the mercury cups, and thus make a momentary bridge, 
over which the current of electricity may pass from pole 
to pole. This method, among others, having been tried, 
was soon abandoned as uncertain and irregular in its re- 
sults ; and the following plan was adopted : 

A small cross of delicate wire was mounted on a short 
axis of the same material, passing through the point of 



INSTRUMENTAL ASTRONOMY. 237 

union of the four arms constituting the cross. This axis 
was then placed horizontal on a metallic support, in Y's, 
■where it might vibrate, provided the top stem of the cross 
could be in some way attached to the pendulum of the 
clock, and the ' ' cross ' ' should thus rise and fall at its 
outer stem as the pendulum swings backward and forward. 
The metallic frame bearing the "cross" also bore a 
small glass tube bent at right angles. This was filled 
with mercury, and into one extremity one wire from 
the pole of the battery was made to dip ; the other 
wire was made fast by a binding screw to the metal- 
lic stand bearing the "cross," and thus every time the 
"cross" dipped into the mercury in the bent tube, the 
electricity passed through the metallic frame, up the ver- 
tical standards bearing the axis of the cross, along the 
axis to the stem, and down the stem into the mercury, 
and finally through the mercury to the other pole of 
the battery. Thus at every swing of the pendulum 
the circuit was made, and a suitable apparatus might, 
by the electro-magnet, record each alternate second of 
time. 

The amount of power required of the pendulum to give 
motion to the delicate wire-cross was almost insensible, 
as the stems nearly counterpoised each other in every 
position. Here, however, there was great difficulty in pro- 
curing a fibre sufficiently minute and elastic to consti- 
tute the physical union between the top stem of the 
cross and the clock pendulum. Various materials were 
tried, among others a delicate human hair, the very finest 
that could be obtained, but this was too coarse ami stiff. 
Its want of pliancy and elasticity gave to the minute 
"wire-cross" an irregular motion, and caused it to re- 
bound from the globule of mercury into which it should 



238 INSTRUMENTAL ASTRONOMY. 

have plunged. After many fruitless efforts, an appeal 
was made to an artisan of wonderful dexterity ; the as- 
sistance of the spider was invoked; his web, perfectly 
elastic and perfectly pliable, was furnished, and this ma- 
terial connection between the wire-cross and the clock 
pendulum proved to be exactly the thing required. In 
proof of this remark I need only state the fact that one 
single spider's web has fulfilled the delicate duty of 
moving the wire-cross, lifting it, and again permitting it 
to dip into the mercury every second of time for a period 
of more than three years ! How much longer it might 
have faithfully performed the same service I know not, 
as it then became necessary to break this admirable 
bond, to make some changes in the clock. Here it will 
be seen the same web was expanded and contracted 
each second during this whole period, and yet never, so 
far as could be observed, lost any portion of its elasticity. 
The clock was thus made to close the electric circuit in 
the most perfect manner; and inasmuch as the resistance 
opposed to the pendulum by the " wire-cross " was a 
constant quantity and very minute, thus acting pre- 
cisely a3 does the resistance of the atmosphere, the 
clock, once regulated with the " cross " as a portion of 
its machinery, moved with its wonted steadiness and 
uniformity. Thus one grand point was gained. The 
clock was now ready to record its own beats automati- 
cally and with absolute certainty, without in any way 
affecting the regularity of its movement. It was early 
objected to the mercurial connection just described, that 
in a short time the surface of the mercury would be- 
come oxidized, and thus refuse to transmit the current 
of electricity ; but experiment demonstrated that the ex- 
plosion produced by the electric discharge at every dip 



INSTRUMENTAL ASTRONOMY. 239 

into the mercury threw off the oxide formed, and left the 
polished surface of the globule of mercury in a perfect 
state to receive the next passage of the electricity. 

So far as known, all other methods are now abandoned, 
and the mercurial connection is the only one in use. 

The time scale. — The clock being now prepared to 
record its beats, accurately and uniformly, the next im- 
portant step was to obtain, if possible, a uniformly moving 
time-scale, which should be applicable to the practical 
demands of the astronomer. 

In case the fillet of paper used in the Morse telegraph 
could have been made to flow at a uniform rate upon its 
surface, the clock could now record its beats, appearing 
as dots separated from each other by equal intervals. 
But it was soon seen that the paper could not be made to 
flow uniformly ; and even had this been possible, a single 
night's work would demand for its record such a vast 
amount of paper that this method was inapplicable to 
practice. After careful deliberation, the " revolving 
disk" was selected as the best possible surface on which 
the record of time and observation could be made. The 
preference was given to the disk over the cylinder for 
the following reasons : — The uniform revolution of the 
disk could be more readily reached. The record on the 
disk was always under the eye in every part of it at the 
same time, while, on the revolving cylinder, a portion of 
the work was always invisible. One disk could be sub- 
stituted for another with greater ease, and in a shorter 
time ; and the measure of the fractions of seconds could 
be more rapidly and accurately performed on the disk 
than on the cylinder. 

After much thought and experiment it was decided to 
adopt "a make circuit*' and ''a dotted scale'' rather than 



240 INSTRUMENTAL ASTRONOMY. 

a " break circuit" and a " linear scale;" and I think it 
will be seen hereafter that in this selection the choice has 
been fully justified in practice. These points being 
settled, the mechanical problems now presented for so- 
lution were the following : First, To invent some machin- 
ery which could give to a disk of, say, twenty inches 
diameter, mounted on a vertical axis, a motion such that 
it should revolve uniformly once in each minute of time; 
and, second, To connect with this disk the machinery 
which should enable the clock to record on the disk each 
alternate second of time, in the shape of a delicate round 
dot. Third, The apparatus which should enable the ob- 
server to record on the same disk the exact moment of 
the transit of a star across the meridian, or the occurrence 
of any other phenomenon. 

The first of these problems was by far the most diffi- 
cult, and, indeed, its perfect solution remains yet to be 
accomplished, though, for any practical astronomical pur- 
pose, the problem has been solved in more than one way. 

The plan adopted in the Cincinnati Observatory may 
be described as follows : — The clock-work machinery em- 
ployed to give to the great equatorial telescope a uni- 
form motion equal to that of the earth's rotation, on its 
axis, offered to me the first obvious approximate solution 
of the problem under consideration. This machinery 
was accordingly applied to the motion of the disk, or 
rather to regulate the motion of revolution, this motion 
being produced by a descending weight, after the fashion 
of an ordinary clock. It was soon discovered that the 
" Frauenhofer clock," as this machine is called, was not 
competent to produce a motion of such uniformity as was 
now required. Several modifications were made with a 
positive gain; but after long study it was finally dis- 



INSTRUMENTAL ASTRONOMY. 241 

covered that when the machinery was brought into per- 
fect adjustment, the dynamical equilibrium obtained was 
an equilibrium of instability ; that is, if from a motion 
such as produced a revolution in one exact minute, it be- 
gan to lose, this loss or decrement in velocity went on 
increasing, or if it commenced to gain, the increment 
went on increasing at each revolution of the disk. Now 
all these delicate changes could be watched with the most 
perfect certainty ; as, in case the disk revolved uniformly 
once a minute, then the seconds' dots would fall in such 
a manner (as we shall see directly), that the dots of the 
same recorded seconds would radiate from the center of 
the disk in a straight line. Any deviation from this line 
would be marked with the utmost delicacy down to the 
thousandth of a second. By long and careful study, it 
was at length discovered, that to make any change in the 
velocity of the disk, to increase or decrease quickly its 
motion, in short, to restore the dynamical equilibrium, 
the winding key of the " Frauenhofer clock" was the 
point of the machinery where the extra helping force 
should be applied; and it was found that a per- 
son of ordinary intelligence, stationed at the disk, and 
with his fingers on this key, could, whenever he noticed 
a slight deviation from uniformity, at once, by slight as- 
sistance, restore the equilibrium, when the machine would 
perhaps continuo its performance perfectly for several 
minutes, when again somo slight acceleration or retarda- 
tion might be required from the sentinel posted aa an 
auxiliary. 

The mechanical problem now demanding solution was 
very clearly announced. It was this : Required to con- 
struct an automaton which should take the place of the 
intelligent sentinel, watch the going of the disk, and ta- 
ll 



242 INSTRUMENTAL ASTRONOMY. 

stantly correct any acceleration or retardation. This, in 
fact, is the great problem in all efforts to secure uniform 
motion of rotation. This problem was resolved theoreti- 
cally, in many ways, several of which methods were exe- 
cuted mechanically without success, as it was found that 
the machine stationed as a sentinel to regulate the going 
of the disk was too weak, and was itself carried off by 
its too powerful .antagonist. The following method 
was, however, in the end, entirely successful. Upon 
the axis of the winding key, already mentioned, a 
toothed wheel was attached, the gearing being so ad- 
justed that one revolution of this wheel should pro- 
duce a whole number of revolutions of the disk. The 
circumference of this wheel was cut into a certain num- 
ber of notches, so that, as it revolved, one of these notches 
would reach the highest point once in two seconds of 
time. By means of an electro-magnet a small cylin- 
der or roller, at the extremity of a lever arm, was 
made to fall into the highest notch of the toothed 
wheel at the end of every two seconds. In case 
the disk was revolving exactly once a minute, the 
roller, driven by the sidereal clock, by means of an 
electro-magnet, fell to the bottom of the notch, and 
performed no service whatever ; but, in case the disk be- 
gan to slacken its velocity, then the roller fell on the 
retreating inclined face of the notch, and thus urged for- 
ward by a minute amount the laggard disk, while, on the 
contrary, should the variation from a uniform velocity 
present itself in an acceleration, then the roller struck on 
the advancing face of the notch, and thus tended slowly 
to restore the equilibrium. Let it be remembered that 
this delicate regulator has but a minute amount of service 
to perform. It is ever on guard, and detecting, as it 



INSTRUMENTAL ASTRONOMY. 243 

does instantly, any disposition to change, at once applies 
its restoring power, and thus preserves an exceedingly 
near approach to exact uniformity of revolution. This 
regulator operates through all the wheel- work, and thus 
accomplishes a restoration by minute increments or de- 
crements spread over many minutes of time. 

With a uniformly revolving disk, stationary in posi- 
tion, we should accomplish exactly, and very perfectly, 
the record of one minute of time, presenting on the re- 
cording surface thirty dots at equal angular intervals on 
the circumference of a circle. To receive the time dots 
of the next minute on a circle of larger diameter, re- 
quired either that the recording pen should change posi- 
tion, or that at the end of each revolution the disk itself 
should move away from the pen by a small amount. We 
chose to remove the disk. To accomplish accurately the 
change of position of the disk, at the end of each revolu- 
tion, the entire machine was mounted on wheels on a 
small railway track, and by a very delicate mechanical 
arrangement accomplished its own change of position 
between the fifty-ninth and sixtieth second of every 
minute. 

The recording pens. — It now remains only to de- 
scribe the simple machinery by which the clock records 
its beats, and the observer makes the record of his obser- 
vation. These instruments are called the recording pens. 
That belonging to the clock is called the time pen ; the 
one used by the observer the observing pen. Thev 
are constructed and operate in the following man- 
ner: A metallic arm is constructed with a short axis, 
perpendicular to its length. The extremities of this axis 
are pivots working in the jaws of a metallic frame, which 
supports the axis of the pen in a horizontal position. The 



244 INSTRUMENTAL ASTRONOMY. 

longer arm of the pen reaches over into the center of the 
disk, and is armed at its extremity with a steel 'point or 
styl s. Upon the long arm of the pen and near the axis 
is located a piece of soft iron denominated an armature, 
and beneath this armature an electro-magnet is firmly 
fixed. This magnet is placed on the circuit closed by the 
wire-cross vibrating with the clock pendulum, and thus, 
at every dip of the cross into the mercury cup, the arma- 
ture of the pen is suddenly drawn down on the head of 
the magnet, and the moment the circuit i3 broken a 
spring acting on the short arm of the pen lifts it from 
the head of the magnet. It is readily seen that in this 
way the stylus is brought down by a sudden shock or 
blow on the material placed on the revolving disk to re- 
ceive the record. The pen is so adjusted that in case 
the armature be simply placed and held by hand on the 
head of the magnet, the steel point of the stylus does not 
quite touch the recording surface on the disk. The elas- 
ticity of the long arm of the pen is, therefore, a matter of 
the greatest moment, for this elasticity causes the pen 
to make a simple dot, by a sudden blow and recoil ; 
whereas were the pen non-elastic, there would be a drag 
for the time during which the magnet holds the pen, 
which would at once destroy the uniformity in the going 
of the disk. 

A pen constructed in precisely the same way, and 
placed at right angles to the former, so that the points of 
the two pens fall in close proximity on the disk, is oper- 
ated by a magnet made by a circuit closed at will by the 
finger of the observer ; and thus he is enabled to throw 
down upon the time scale a dot, which, falling between 
some two-second dots on the disk, records the exact in- 
stant of any phenomenon under observation. 



INSTRUMENTAL ASTRONOMY. 245 

When the disk is filled, we have only to lift it from its 
socket and replace it with a new disk. To read the time 
scale it is only necessary to mark on the disk from the clock 
face the time denoted by any one dot ; for example, 12h. 
15m. 00s. The circle next outside will be 12h. 16m., the 
next circle 12h. 17m., &c. ; while the first or marked radius 
of dots will be the second of all the minutes, the next 
in order will be the second, the next the fourth, and so 
on to the 58th and second again. Thus we read the 
scale as rapidly as we read a clock face, for the hour, min- 
ute and second ; and it only remains to construct a ma- 
chine for measuring the fractions of seconds. 

The angular time micrometer. — This instrument 
is very simple. Take a common carpenter's two-foot 
rule ; cut away the inner portion of one of the legs for 
two-thirds of its length, and insert a piece of plane glass ; 
draw from the centre of the joint with a diamond point, 
on the under surface of this glass, a delicate straight line, 
and blacken by rubbing in black lead pencil. The arms 
of this micrometer are a little longer than the radius of 
the disk. To the left hand arm, at its outer extremity, 
attach a small brass arc, divided into seconds and tenths, 
and make it, say, 2\ seconds in length. When the two 
legs are closed the black line on the glass will read on 
this scale of seconds. At the joint drill a small hole, and 
at the center of the disk to be measured erect a small 
vertical pin to fit this hole. Lay the instrument on the 
disk, the pin being inserted in the hole, and thus the 
fractions of seconds may be measured with any degree of 
precision. 

Such is an outline of the machinery now in use in the 
Dudley Observatory at Albany, and at the Cincinnati 
Observatory. 



246 INSTRUMENTAL ASTRONOMY. 

As we have seen, in the old method of transits the at- 
tention of the observer was divided among many objects. 
He was compelled to keep up the counting of the clock 
beat ; to estimate the space passed over by the star under 
observation in a second of time ; to subdivide this space 
by estimation into tenths; to write down in his note- 
book the observed moment of transit across each of the 
wires, and all this while his eye continued to follow the 
movement of the object under observation. To give the 
observer time to make his record, the spider's lines or 
wires were necessarily separated by such an interval 
from each other that several seconds would be required 
by the star to pass from one to the other, and thus but 
few wires could be employed in transit observations. 

In the new method the observer is released from all 
responsibility with reference to time, counting of clock 
beat, estimation of spaces, or entries in note-book. The 
clock records its own beat, and the observer has nothing 
to do but touch a magnetic key at the exact moment in 
which his star is bisected by the meridian wire. This 
touch records the moment of observed transit, and as this 
record is accomplished almost instantaneously, the ob- 
server is ready to record the transit across the next wire, 
and thus the interval between the wires may be greatly 
reduced, and their number extended almost indefinitely. 
While in the old method long practice was required to 
make an accomplished observer (the best of whom could 
not record more than the transits on seven wires), in the 
new method a few nights of practice gives all desirable 
experience, and the observer may record the transits 
across as many as fifty wires, should so large a number 
ever be desirable under any circumstances. It is found 
in the use of this method that erroneous habits of obser- 



INSTRUMENTAL ASTRONOMY. 247 

vation may either be entirely avoided or detected, and 
thus corrected. It furnishes the means of measuring 
with great accuracy the value of personal equation, and 
has demonstrated, indeed, that the large differences exist- 
ing between observers, amounting in some instances to a 
whole second of time, are not due to physiological consti- 
tution, but almost entirely to false habits of observation. 
It has furnished the means of measuring the amount of 
time which elapses between the occurrence of any phe- 
nomenon falling within the grasp of the senses of sight 
and hearing, and the possible record by the touch of a 
magnetic key. In this operation there are three distinct 
processes, the sense of sight, for example, conveys to the 
brain information of the occurrence of the external phe- 
nomenon ; the mind thus perceives, and the will issues an 
order to the nerves to record ; the nerves execute this 
order. Thus far it has been impossible to ascertain the 
amount of time occupied in each of these processes, but 
the sum of the times, or that elapsing between the mo- 
ment of occurrence of a phenomenon and its record, has 
been measured both for the sense of sight and the sense 
of hearing, in a large number of persons of both sexes 
and of all ages. From these experiments it has been as- 
certained that while different individuals present promi- 
nent and marked differences, these differences are only 
found to exist in the hundredths of a second of time, and 
not, as has been imagined, in whole seconds. In con- 
ducting these experiments it was ascertained that all ob- 
servers, without a single exception, in attempting to 
mark the moment at which a star crossed a wire, antici- 
pated the moment of transit, and the recorded time was 
thus in advance of the true time. Having learned this 
fact, the observer is placed upon his guard, and is fur- 



248 INSTRUMENTAL ASTRONOMY. 

nished with the means of correcting this false habit, and 
of bringing himself up to a standard of positive accuracy. 
Another advantage derived from this mode of observation 
arises from the fact that it imposes but a slight tax upon 
the nervous system, and hence an observer is able to 
continue his work without exhaustion for a much longer 
period of time. 

We have mentioned that one of the most hidden 
sources of error lies in the uncertainty of the rate of 
going of the clock. The old methods furnish the means 
of ascertaining with comparative accuracy how much the 
clock has lost or gained in twenty-four hours ; and if this 
quantity should amount only to a fraction of a second, 
it is almost impossible to assert that this loss or gain 
may not have occurred even a hundred times, or pos- 
sibly a thousand times during the twenty-four hours. 
By causing two or more clocks to record their beats 
upon the same time-scale, the new method furnishes the 
means of inter-comparison between these clocks, even 
from second to second, if required, and thus from a 
record of this kind may be obtained a positive standard 
of time. 

The electro-magnetic method of observation in connec- 
tion with the system of telegraphic wires, now extended 
over nearly all the civilized world, furnishes a very rapid 
and exact method of determining the difference of longi- 
tude between any two points. This difference of longi- 
tude is nothing more than the time which elapses from 
the transit of a star across the meridian of one place until 
it crosses the meridian of the other place. In case the 
two observatories whose difference of longitude is required 
are connected by telegraph, and are furnished with the 
electro-magnetic apparatus, the observer in the eastern 



INSTRUMENTAL ASTRONOMY. 249 

observatory may send to his correspondent by telegraph 
the moment of transit of the star across his own meridian. 
He will receive in return by telegraph the moment the 
same star crosses the meridian of the western observatory, 
and in case the observations are perfectly made, transmit- 
ted with infinite velocity along the wires, and recorded 
with perfect accuracy, the result will be absolutely per- 
fect. The common errors of observation are readily elimin- 
ated, the errors of recording, in like manner, are easily 
detected and measured, and the only matter of difficulty 
which remains is to ascertain whether the message sent 
along the wire travels at a finite rate, and if so, to deter- 
mine what this rate may be. The conversion of time 
into space, and the delicacy of the machinery now em- 
ployed in recording and subdividing time, has furnished 
the means of measuring the velocity with which signals 
are transmitted along the wires of the telegraph. No 
doubt this velocity is modified by a variety of circum- 
stances, and may depend upon the direction in which the 
telegraphic wire is laid, the season of the year, the tem- 
perature of the earth and atmosphere, but none of these 
causes can interfere to mar the accuracy of the work em- 
ployed for longitude purposes; for there is no difficulty in 
determining the exact velocity with which the signals are 
transmitted by the wires at the time of observation. 
These are a few among many advantages which have been 
gained by the conversion of time into space, and the ap- 
plication of this principle to the observation of astrono- 
mical transits. 

The author has attempted to add something to the 
facility and accuracy of the determination of north polar 
distances, the second great element employed in fixing 
the place of a heavenly body. As already explained, 



250 INSTRUMENTAL ASTRONOMY. 

this element is reached by the division of a circle attached 
to the axis of the transit, and the accuracy of the work 
depends upon the perfection of these divisions, the per- 
manence of the figure of the circle, the permanence in 
the place of the reading microscopes, and the precision 
attainable in reading the subdivisions of the circle. As 
the errors which arise from these diiferent sources are 
found to be comparatively large, for the measurement of 
small differences of north polar distances, or small arcs 
of space, resort has been had to other and more delicate 
mechanical contrivances, hence the invention and con- 
struction of the various micrometers now in use, all of 
which depend for their accuracy upon the performance 
of a micrometer screw. Very extended experiments with 
these instruments first created a doubt in my own mind 
as to the accuracy with which the micrometer screw 
would repeat its own measures. This doubt, added to the 
fact that the measurements by the micrometer were very 
slow and tedious, gave rise to the effort which has resulted 
in the construction of a new system whereby differences 
of north polar distance may be determined with great 
rapidity and precision, which principle can readily be ex- 
tended to the determination of absolute north polar dis- 
tances. A description of the machinery employed for 
this purpose may be found elsewhere. We are only 
concerned here to notice some of the possible advan- 
tages of this new method of north polar distances. I 
will only state that the machinery employed in all its 
joints and connections is of the simplest kind, and every- 
where visible to the eye. There is no concealed portion, 
as in the screw micrometer, no joints to grow imperfect 
by wearing, and no strong resistance to change the figure 
of any part of the machinery. If the tube of the tele- 



INSTRUMENTAL ASTRONOMY. 251 

scope, loaded as it is with the weight of the object glass 
and eye-piece, and its own weight, can be depended upon 
to retain its figure without a counterpoise, it is absolutely 
certain that the declination arm, which in the new method 
is attached to the axis of the transit, if perfectly counter- 
poised and bearing no weight whatever, can be relied upon 
to retain its figure. The lower extremity of this arm, 
moving as it does in north polar distance, with the line 
of collimation of the telescope, by a connecting bar, gives 
motion to the axis of the reading microscope, which, 
being directed to a distant scale, magnifies in a very high 
ratio by mechanical means the arc through which the 
transit revolves in the plane of the meridian. Thus it 
will be seen that this new method is nothing more than 
the use of a mechanical magnifier, and the only question 
is, can the scale be so divided as to read seconds of arc, 
and can it be made of invariable length? There is 
little difficulty in accomplishing both of these objects, 
for scales have already been divided with such precision 
that no error amounting to the hundredth part of a single 
second of arc could possibly exist ; and in order to re- 
tain an invariable length in the scale all that is necessary 
is to grade it upon a surface constituting one face of a 
rectangular tube ; fill this tube with water and broken 
ice, and thus a permanent temperature of 32° may 
be had for any length of time. To measure the exact 
value of the divisions on the scale we have only to em- 
ploy these divisions in measuring around the entire cir- 
cumference of the circle attached to the axis of the tran- 
sit Suppose the length of the scale to be sixty minutes 
approximately, then if this length is contained 360 times 
in the whole circumference, its approximate value be- 
comes its absolute value, and at all events this experiment 



252 INSTRUMENTAL ASTRONOMY. 

furnishes the means of determining the absolute value. 
Thus while the circle furnishes the means of measuring 
the scale, the scale furnishes in return the means of 
measuring the subdivisions of the circle. These amount 
only to 360, and may be reduced even to the fifth part 
of this number, should practice prove this reduction de- 
sirable. This small number of divisions can rapidly be 
read up with a scale of invariable length, and by per- 
forming this reading at temperatures widely different a 
correction for temperature may be determined with great 
exactness. In the old circle, as there are no less than 
ten thousand divisions, and as there exists no permanent 
scale for the reading of these divisions, it becomes almost 
impossible to learn their actual values and to tabulate 
their errors, hence astronomers have been compelled to 
rely to a great extent upon the assumed accuracy of the 
subdivisions of their circles, as received from the hands of 
the manufacturer. 

By a combination of the electro-magnetic method, with 
the new method of measuring north polar distances, a very 
simple, convenient, and accurate instrument is obtained 
for recording the places of the stars or other heavenly 
bodies with great rapidity and exactitude, rendering it 
possible to construct, in a comparatively short time, a 
very extended and exact catalogue of the places of all the 
fixed stars, clearly visible, with any optical power. 

We have thus presented a rapid sketch of the old and 
new methods of fixing the elements for the determination 
of the heavenly bodies, it only remains in this connec- 
tion to speak of the optical power of the telescope. 

These instruments are divided into two great classes, 
called reflect big and refracting telescopes. In the re- 
flecting telescopes the rays of light from the external ob- 



INSTRUMENTAL ASTRONOMY. 253 

ject, passing down the tube of the telescope, fall upon a 
metallic mirror or speculum, whose surface, perfectly 
polished, has the figure of a paraboloid of revolution, 
Being reflected by this surface, the rays of light are con- 
centrated at a certain point, called the focus, where an 
intensely luminous image of the object is formed. This 
image is then examined by a magnifying glass or eye- 
piece, and its dimensions expanded to any required de- 
gree. 

In the refracting telescope the light falls upon what 
is called the object-glass, a powerful lens, which con- 
centrates, by refraction, the rays of light which pass 
through it, thus forming an image of the object at the 
focal point. This image is then examined, as in the re- 
flecting telescope, by eye-piece3 having different magni- 
fying powers. Hitherto it has been found impracticable 
to construct object-glasses of any very considerable dia- 
meter, the largest of these glasses in use not exceeding 
sixteen to twenty inches in diameter. These narrow 
limits do not exist, however, in the construction of the 
metallic specula which belong to the reflecting telescope ; 
and hence we find gigantic instruments have been con- 
structed by different observers, one of which, now in use 
by Lord Ross, has a speculum of no less than six feet in 
diameter, with a focal length of fifty- two feet. Such 
immense instruments, requiring ponderous machinery for 
their management, are not well adapted for that kind of 
observation having for its object to determine the places 
of the heavenly bodies. Their use has been rather con- 
fined to examinations of the planets, double stars, clus- 
ters, and nebulae, demandiog a large amount of light 
rather than a perfect definition or exactitude in measure- 
ment. It is true, that in the hands o( Lassell, of Liver- 



25i INSTRUMENTAL ASTRONOMY. 

pool, we find the reflecting telescope performing admir- 
ably in the routine work of an observatory. But these 
instruments are comparatively small, their dimensions 
not much exceeding those of the largest refractors. 

There are two qualities which distinguish the telescope, 
the space-pe net rating power and the power of definition. 
The first of these depends exclusively upon the amount 
of light received and refracted, or reflected to the focus, 
and thus forming the image. In case all the light fall- 
ing upon the object-glass or speculum could be concen- 
trated in the formation of the image, then the space-pene- 
trating power of telescopes would be exactly proportioned 
to the diameters of their apertures, and we can compare 
then, readily, the space-penetrating power of different 
instruments, not only among themselves, but directly 
with the space-penetrating power of the human eye. The 
diameter of the pupil of the eye determines the amount 
of light which can enter and form the image, just as the 
diameter of an object-glass in a telescope determines the 
amount of light which in that instrument forms the focal 
image; hence, if we desire to know how many times 
deeper a telescope can penetrate space than the eye, we 
have only to learn how many times the area of the ob- 
ject-glass exceeds that of the pupil of the eye. We shall 
have occasion hereafter to employ this principle when we 
come to examine the relative distances to which the ne- 
bulae and clusters are sunk in space. 

We have only spoken of the mounting of the transit, 
with its attached circle, for reading north polar distances. 
This instrument revolves only, as we have seen, in the 
plane of the meridian, and of course no object can be 
seen with the transit except when in the act of passing 
the meridian line. 



INSTRUMENTAL ASTRONOMY. 255 

A telescope mounted in such a manner that it can be 
directed to any point of the heavens, is called an extra- 
meridional instrument, and of these the equatorial is 
the most used, and is the best adapted for all observations 
off the meridian. The tube of the telescope is carried by 
a heavy metallic casting, very firm and strong, which is 
made fast to a metallic cylinder, through which passes a 
steel axis, called the equatorial axis. The metallic cylin- 
der is also screw-bolted to the extremity of a heavy steel 
axis, so placed on its supports as to lie parallel to the 
earth's axis. These supports rest on heavy metallic 
plates, bolted to a massive stone pier, called the "foot 
of the instrument," which, in turn, is placed on the top 
of a heavy pier of masonry, resting on a rock foundation, 
or something equally solid, and entirely disconnected 
from the building. 

The instrument is so counterpoised in all its many 
parts as to be readily moved either on its polar or equa- 
torial axis, and may thus be directed to any point of the 
celestial sphere. To enable the observer to follow the 
object under examination these telescopes are usually fur- 
nished with a species of clock-icork, which causes the 
instrument to revolve round its polar axis with a velocity 
equal to that of the earth's rotation, causing it to follow 
a heavenly body and to hold it steady in the field of view 
for any required period of time. 

Without extending further our notice of the instru- 
ments employed in reaching the data required in astrono- 
mical investigation, we will now return to our examination 
of the bodies which compose the sun's retinue, and shall 
proceed in our plan, preserving the order of distance 
from the sun. 

The interruption which was made after closing the 



256 INSTRUMENTAL ASTRONOMY. 

discussion of the system of Saturn, to introduce to the 
student the laws of motion and gravitation, and the in- 
struments employed in astronomical measures, was neces- 
sary to a full comprehension of the extraordinary inves- 
tigations which are now to follow. We are hereafter to 
treat the planets and their satellites as ponderable bodies, 
mutually affecting each other, and all subjected to the 
dominion of the laws of motion and gravitation. 



CHAPTER XII. 



DISTANCE FROM THE SUN. 



Accidentally Discovered by Sir "William Hersciiell. — Announced as a 
Comet. — Its Orbit proved it to be a Superior Planet. — The Elements 
of its Orbit Obtained. — Arc of Retrogradation. — Period of K evolu- 
tion. — Figure of the Planet. — Inclination of its Orbit.— Six Satel- 
lites Announced by the Elder Hersciiell. — Four of these now 
Recognized.— Their Orbital Planes and Directions of Revolution 
Anomalous. — Efforts made to Tabulate the Places of Uranus Unsuc- 
cessful. — Tins Leads to the Discovery of a New Exterior Planet. 



It was remarked at the close of our investigation of the 
Saturnian system that this planet inclosed by its orbit 
all the objects belonging to the solar system which were 
known to the ancients, and whose phenomena, as observed 
and recorded in all time, furnished the data for the dis- 
covery of Kepler's laws and the law of universal gravi- 
tation, as finally revealed by Newton. While many of 
the modern astronomers, from an examination of the 
inter-planetary spaces, had ventured to suggest the pro- 
bable existence of a large planet revolving in an orbit 
intermediate between thoso of Mars and Jupiter 3 no 
one had ventured to predict the possible discovery of 
planets lying exterior to the mighty orbit ot % Saturn. 
From the very dawn of astronomy this planet had 
held the position of sentinel on the outposts of the 
planetary system, and many strong minds had long en- 



258 URANUS. 

terta'ned the opinion that no other bodies existed exterior 
to the orbit of Saturn forming a part of the scheme of 
worlds revolving around the sun. Such, indeed, was the 
prevalence of this opinion that when, in 1781, Sir William 
Herschell, in a course of systematic exploration of the 
heavens, discovered an object having a well-defined plan- 
etary disk, and whose movement among the fixed stars 
became measurable, even at the end of a few hours, he 
did not even suspect this new object to be a planet, but 
announced to the world that he had discovered a most 
extraordinary comet, without any of the usual haziness 
which attends these bodies, but presenting a clear and 
well defined planetary disk. 

This newly-discovered object soon attracted universal 
attention. It was observed at the royal observatory at 
Greenwich, and the then astronomer royal, Dr. Marke- 
lyne, was the first to suspect its planetary character. 
Efforts were made by several computers to give to the 
new comet, as it was called, a parabolic orbit ; this, how- 
ever, was found to be impossible, and it was very soon 
found that the newly-discovered object was revolving 
around the sun in an orbit nearly circular in form, lying 
in a plane, nearly coincident with the ecliptic, and com- 
pleting its mighty revolution in a period of no less than 
eighty-two years. It must be remembered that these 
extraordinary discoveries and announcements were made 
at the end of a very short examination, while the 
periods of revolution of all the old planets had been 
obtained from actual observation, through long centuries 
of patient watching. The periodic time of this last dis- 
covered of all the planets, which, by the old method of 
watching its return to the same fixed star, could not have 
been determined in less than eighty-two years, and even 



URANUS. 259 

then only approximately, was, by the new method, based 
upon the law of universal gravitation, guided by the re- 
sults of a few nights of accurate observation, and worked 
out by the powerful formulae of analytic reasoning, 
given to the world with accuracy after only a few 
months of investigation. This is the first illustration 
of the change wrought in the whole movement of astron- 
omical science by the great discoveries of Newton, and 
by the almost equally extraordinary step accomplished 
by Descartes, in fastening the powers of analysis upon 
geometry. All the circumstances of motion of this planet 
were rapidly investigated ; the eccentricity of its orbit ; 
the position of its perihelion ; the inclination of its orbit 
to the plane of the ecliptic ; the position of its line of 
nodes ; the measure of its actual diameter ; the determ- 
ination of its various distances from the sun, all these 
and many other peculiarities were accurately determined 
from actual observation and computation. These facts 
strike us with the more astonishment when we reflect that 
the planet Uranus is removed to a distance of eighteen hun- 
dred millions of miles from the sun, and that, although 
its actual diameter is thirty-Jive thousand miles, it is ab- 
solutely invisible to the naked eyed, and, when seen 
through the most powerful telescope, presents a disk of 
only t\\Q Jive hundredth part of the apparent diameter of 
the sun. At such an immense distance it has been im- 
possible thus far to determine anything with reference 
to the precise figure of Uranus. The discoverer of the 
planet thought that he saw a flattening at the polos, but 
subsequent observation has not confirmed this announce- 
ment. We have only, therefore, analogy to induce ua 
to believe that this planet, like all the Others, rotates 
upon an axis, and that, consequently, its figure is that 



260 URANUS. 

of the elipsoid and not of the sphere. The immense mag- 
nitude of the orbit of Uranus, when compared with that 
of the earth, causes this planet to retrograde over an arc 
of only 3° 36', but the duration of the retrograde motion 
extends over a period of no less than one hundred and 
fifty-one days. No telescope has yet been able to discern, 
upon the surface of Uranus, any spot or belt, or any well- 
defined point, distinguished from the entire surface, so 
that we have no means, thus far, of fixing the period of 
rotation upon its axis. The amount of light and heat 
received by Uranus, admitting the law of diminution, 
which seems to govern these elements, could only be the 
quarter part of that received by the planet Saturn, while 
the apparent diameter of the sun, as seen from Uranus, 
would be less than the thirtieth part of his diameter, as 
seen from the earth. 

This planet is surrounded by at least four satellites. 
Two others were announced by Sir Wm. Herschel, who 
not only gave their distances but their periods of revolu- 
tion, yet no telescope has since been able to detect these 
minute points of light, and their very existence is now 
doubted by many of the best observers. Four of the 
satellites had been studied, with much care, and their 
periods of revolution and their mean distances had been 
well determined. Of these, the second and fourth are 
most readily seen, and different astronomers have obtained 
results which agree with each other within comparatively 
small limits of error. Thus, the elder Herschel fixed 
the period of revolution of the second satellite, in the order 
of distance, at 8d. 16h. 56m. 5s. Sir John Herschel 
made the same period twenty-six seconds longer. Dr. 
Lamont, of Munich, obtained, for this same period, 
a value of 8d. 16h. 56m. 28s.5. The period of revolu- 



URANUS. 261 

tion of the fourth satellite, in the order of distance, as de- 
termined by Lamont, amounts to 13d. llh. 07m. 06s. 3. 
The period of revolution of the nearest satellite is about 
five days and twenty-one hours, while the third satellite 
in order of distance performs its revolution in a period of 
about eleven days. These are among the most difficult 
of all the objects revealed to the eye by telescopic power. 
After Sir Wm. Herschell no one for many years was 
able to see any of these satellites, the forty-foot reflector 
of Herschel having gone into disuse. In 1828, Sir John 
Herschel, after many unsuccessful attempts, by confin- 
ing himself in a dark room for many minutes previous to 
observation, and thus giving to the eye great acuteness, 
succeeded in detecting two of these satellites. In 1837, 
Lamont, with the powerful refractor of the royal observa- 
tory of Munich, managed to follow, with tolerable cer- 
tainty, the two larger satellites, and occasionally obtained 
glimpses of two others. 

At this time there are four or five telescopes in the 
world capable of showing these four satellites, under 
favorable circumstances. I have frequently seen two of 
them with the Cincinnati refractor, but they are certainly 
objects of great difficulty, and only to be discerned under 
the most favorable circumstances in the observer, and 
under the best possible conditions of atmosphere. 

Enough, however, has been determined with reference 
to these four satellites to warrant the assort ion of a fact 
of most extraordinary character, and nowhere else to bo 
found in the whole range of the solar system, namely. 
that their orbits are nearly perpendicular to the plane 
of the ecliptic, and that their motions are retrograde. 
We have seen that all the planets revolve in orbits whoso 
planes are nearly coincident with the plane of the eclip- 



262 URANUS. 

tic ; that they all revolve in the same direction around the 
sun ; that the sun and all the planets rotate on their 
axes in the same direction in which they revolve in their 
orbits. We have found, in like manner, that all the satel- 
lites of every planet revolve around their primaries in 
the same direction, and in planes nearly coincident with 
the planes of the equators of their primaries ; so that it 
became a settled opinion that there was but one direction 
in which any rotation or revolution could be performed 
by a member of the planetary system ; and thus when the 
asteroids were discovered, although there were consider- 
able deviations in the angles of the inclination of the 
planes of their orbits from those of the old planets, yet 
in every instance their motions are found to be direct. 
These satellites of Uranus present, then, the only example 
of retrograde movement among the legitimate members 
of the solar system. We shall see hereafter that among 
the comets (which may be regarded as satellites of the 
sun) there are a few which present this same anomaly of 
retrograde movement, yet this is not nearly so surprising 
as to find this anomalous motion among the satellites of 
a primary planet. We shall return to the consideration 
of this subject when we come to discuss the cosmogony 
of the universe. 

If we recall to mind the relations which exist between 
the distances and periodic times of Uranus and Saturn, 
we shall find that these two planets, when nearest to each 
other, or when in conjunction, are separated by a distance 
of about nine hundred millions of miles. When most 
remote from each other, this distance of separation is in- 
creased by the whole diameter of the orbit of .Saturn, or 
by eighteen hundred millions of miles, as will be readily 
seen from the figure, in which S represents the sun, 



URANUS. 



263 



A and B the places of Saturn and Uranus when in con- 
junction, while B' represents the place of Uranus in the 
opposite part of its orbit, or when in opposition to the sun. 
Thus the distance between the planets when located at 




A and B is just equal to the interval between their 
orbits, while this interval is increased as Uranus recedes 
from B up to the time that it reaches B', and on reaching 
this point, Saturn being supposed to occupy the point A, 
the two planets will be separated by a distance of about 
twenty-seven hundred millions of miles. Since Saturn 
performs its revolution in about twenty-nine years and a 
half, and Uranus performs its revolution in about eighty- 
two years, the interval from one conjunction to the next 
is readily computed to be about forty years. 

This extraordinary change of distance produces a cor- 
responding change in the reciprocal influences exerted by 
these planets upon each other. The same remark is ap- 
plicable to the configurations of Jupiter and Uranus, and 
may be extended indeed to all the planets. Thus we 
perceive that the greatest possible effect to draw Uranus 
closer to the sun will be produced when all the planets 



264 URANUS. 

lie on the same straight line, and on the same side of the 
sun. 

The prevalence of the law of universal gravitation, 
whereby every particle of matter in the universe feels the 
attraction of every other particle, unites all the planets and 
their satellites into one grand scheme of revolving worlds, 
in which each is subjected to the influence of all the 
others. After the discovery of Uranus an effort was 
made to assign to this planet a curve whose magnitude 
and position were derived from observations embracing 
but a small portion of its orbit. This, of course, was 
a matter of necessity, for even one revolution has not 
yet been completed by Uranus since the date of its dis- 
covery in 1781. The orbit assigned to the planet was 
sufficiently accurate to trace backward its movement 
among the fixed stars. This was done in the hope that 
the planet might have been seen and its place recorded 
as a fixed star by some of the early astronomers. If it 
should happen that the computed place of the planet 
should coincide with the recorded place of a star of the 
same magnitude as the planet, then a suspicion would 
arise that this star and the planet were one and the same 
body. If on directing the telescope to the point once 
occupied by the star the place should be found vacant, 
this evidence would be almost conclusive that the sup- 
posed star was actually the planet. By an examination 
of this kind it was found that the planet Uranus had been 
observed, and its place carefully recorded by no less than 
three astronomers, each of whom had seen it several 
times, without any suspicion of its planetary character. 
The astronomer Flamsteed was the first who had mistaken 
this planet for a star nearly ninety years before its dis- 
covery by Sir William Herschell. It was subsequently 



URANUS. 265 

observed by Bradley, by Mayer, and by Le Monnier, 
who fixed its place no less than twelve times during the 
period from 1750 to 1771. These ancient observations 
furnished an opportunity to test the accuracy of the com- 
puted elements of the orbit of the new planet, and to cor- 
rect these elements in case they were found to be sensibly 
in error. This work was executed in a most faithful and 
exact manner by M. Bouvard, who also computed tables 
predicting the places of Uranus for many years in ad- 
vance. It was supposed with reason that these tables 
would point out the places of Uranus with the same cer- 
tainty as those of Saturn and Jupiter, computed by the 
same astronomer, gave the places of these planets. In 
this the hopes of the astronomical world were disap- 
pointed, and this extraordinary discrepancy between com- 
putation and observation gave rise to the discovery of an 
exterior planet, as we shall now relate. 

12 



CHAPTER XIII. 



THE ORDER OF DISTANCE FROM THE SUN. 



Uranus Discovered by Accident. — Ceres by Research with the Telescope. 
— Rediscovered by Mathematical Computation. — The Perturbations 
op Uranus. — Not Due to any known Cause. — Assumed to Arise from 
an Exterior Planet.— Nature of the Examination to find the Un- 
known Planet. — Undertaken at the same time by two Computers. — 
Computation Assigns a Place to the Unknown Planet. — Discovered 
by the Telescope. — Discoveries Eesulting. — A Satellite Detected. — 
The Mass of Neptune thus Determined.— Neptune's Orbit the Circum- 
scribing Boundary of the Planetary System. 



The discovery of Neptune is undoubtedly the most 
remarkable event in the history of astronomical science — 
an event without a parallel, and rising in grandeur pre- 
eminently above all other efforts of human genius ever put 
forth in the examination of the physical universe. 

The planet Uranus was discovered by the aid of the 
telescope, not exactly by accident, but still without any 
expectation on the part of the discoverer that his examina- 
tion of the fixed stars would result in the addition of a 
primary planet to the system. Indeed, as we have seen, 
so little did the astronomical world then anticipate the 
discovery of a new planet that the announcement by Sir 
William Herschel that he had detected a most remarkable 
comet was accepted on all hands, and it was only con- 
tinued observation that finally compelled astronomers to 



NEPTUNE. 267 

accept the new object as a planet. In the case of the 
discovery of the first asteroid we find a systematic organ- 
ization of astronomical effort to detect a body whose exist- 
ence was conjectured, on the single ground of the har- 
mony of the universe, or that the law of interplanetary 
spaces, interrupted between Mars and Jupiter, would be 
restored by finding a planet revolving within that vast 
interval. Hence a search was commenced which con- 
sisted in examining every star in the region of the eclip- 
tic, to ascertain whether its place was already laid down 
on any known map or chart of the heavens. Now it is 
evident that if it were possible to make a perfect daguer- 
reotype of any region of the celestial sphere, say to-night, 
and the same could be effected on the following night, 
the comparison of these two pictures would exhibit to the 
eye any change which may have occurred in the interval 
from the one picture to the other ; and hence if a star 
was found on the second and not on the first picture, 
this star might fairly be suspected to be a planet, or the 
same suspicion would attach to a star found on the first, 
but missing on the second picture. Now, a map of the 
heavens, so far as it includes the correct places of the 
stars, answers our purpose quite as well as the daguerreo- 
type, and any star found in a region well charted, but 
not laid down on the map, may be fairly suspected to be 
a planet. A few hours of examination will show it to be 
at rest or in motion. If in motion, then its planetary 
character is decided. 

This method of research has been employed in the dis- 
covery of all the asteroids, and there is hut one example 
in which a more powerful and searching examination bo- 
came necessary. This was in the ease o( the asteroid 
Ceres, which, as we have seen, was discovered by Piaui, 



268 NEPTUNE. 

at a time when but few observations could be made previ- 
ous to its being lost in the rays of the sun. For a long 
time it seemed almost a hopeless task to undertake the 
re-discovery of the planet, as the telescope would be com- 
pelled to grope its way slowly round the heavens, in the 
region of the ecliptic, comparing every star with its place 
in the chart. In this dilemma mathematical analysis 
essayed to erect a structure on the narrow basis of the 
few observations obtained by Piazzi, whereon the instru- 
mental astronomer might stand and point his telescope to 
the precise point occupied by the lost planet. The genius 
of Gauss succeeded in this herculean task, and when the 
telescope was pointed to the heavens in the exact place 
indicated by the daring computor, there, in the field of 
view, shone the delicate and beautiful light of the long- 
lost planet. 

This was certainly a most wonderful triumph of analytic 
reasoning, yet in this case the planet had been discovered, 
was known to exist, and had been observed over 4° out 
of the 360° of its revolution round the sun. On this 
basis of 4° it was possible to rise to a knowledge of the 
planet's position at the end of a few months of time. 

The case of the discovery of Neptune is entirely differ- 
ent. Here no planet was known to exist, no telescopic 
power, however great, had ever seen it. For ages it had 
revolved round the sun in its vast orbit, far beyond the 
utmost known verge of the planetary system, unfathom- 
ably buried from human gaze and from human knowl- 
edge. No sage of antiquity had ever dreamed of its ex- 
istence. The fertile brain of even Kepler had failed to 
imagine its being, and the powerful penetration of New- 
ton's gigantic intellect had failed to pierce to the far off 
region inhabited by this unknown and solitary planet. 



NEPTUNE. 269 

Indeed, with the knowledge which existed prior to the 
discovery of Uranus, no human genius, however mighty, 
could have passed the tremendous interval which separates 
the orbits of Saturn and Neptune from each other. The 
discovery of an intermediate planet was requisite to fur- 
nish a firm foothold to him who would adventure to pass 
a gulf of not less than 2,000 millions of miles at its nar- 
rowest place. 

We shall now proceed to relate the circumstances 
which led to the discovery of Neptune. As already 
stated, a careful and elaborate study of the orbit of 
Uranus had been accomplished by M. Bouvard, and 
tables giving the computed places of this planet had been 
prepared by the same astronomer. It was not antici- 
pated that these tables would be absolutely perfect, even 
if based on perfect observations. We must remembei 
that each body of the solar system affects every other, 
and hence no single set of observations are sufficient to 
give a perfect orbit. In case all the other worlds were 
blotted out of existence, and there remained only the 
sun and Uranus, then three perfect observations of the 
planet's place would suffice to determine positively all 
the elements of its orbit, and fix forever all the circum- 
stances of its motion. We shall call the figure of the 
orbit of Uranus, obtained under the above hypothesis, 
the normal figure, and the ellipse which it would de- 
scribe about the sun, under the above circumstances, the 
normal ellipse. If now we introduce another planet 
into our system, as, for example, Saturn, it is possible, 
as we have already seen, to compute the exact amount of 
power exerted by Saturn to disturb the movements of 
Uranus, and to change the figure of its orbit. In like 
manner, by adding successively all the interior planets. 



270 NEPTUNE. 

it is possible to compute the perturbations that each pro- 
duces upon the orbit of any particular one, until, finally, 
by using all the power of analytic reasoning, the human 
mind may reach to a complete knowledge of all possible 
derangements produced by the combined action of all ex- 
isting known causes of perturbation. 

Supposing our knowledge in this way to become per- 
fect as to the movements and orbit of Uranus, we can 
then predict its places in all coming time, and these pre- 
dictions, being arranged in tabular form, may be verified 
by comparison in after years with the observed places of 
the planet. If now a new planet were added to the sys- 
tem, revolving in an orbit exterior to that of Uranus, 
perturbation would arise from the introduction of this 
disturbing body into our system which would at once 
cause the planet to deviate from its predicted track, and 
the observed and computed places would no longer agree. 

We can perceive at once, from this statement of the 
problem, that these very discrepancies between the old 
track and the new one, pursued by the planet, would 
give us a clue whereby it might become possible to de- 
termine, in space, the position of the disturbing body. 

Difficult and incomprehensible as the above problem 
may appear, it is far less difficult than the one actually 
presented in nature. We have supposed the normal 
ellipse, described by Uranus, to be known, whereas, in 
reality, this very ellipse had to be determined by a train 
of reasoning of the most searching and powerful charac- 
ter, while the whole problem was almost hopelessly em- 
barassed by the fact that the movements of Uranus were 
actually being disturbed all the time by the unknown 
body whose position in space was required. As the 
normal orbit could only be determined by a series of ap- 



NEPTUNE. 271 

proximations, based upon the observed places of the planet, 
it was impossible, in any one of these approximations, to 
free Uranus from the disturbing effects of the unknown 
body. It was only, therefore, by comparing with each 
other the results reached by these successive approxima- 
tions to the orbit of Uranus that it became manifest that 
no increase of accuracy was beiug reached by these suc- 
cessive efforts, and after every known cause of disturb- 
ance had been carefully taken into account, a grand con- 
clusion was finally reached that 'no satisfactory account 
could be rendered of the movements of Uranus by the 
combined effects of all known disturbing causes. 

To reach this conclusion required investigations of the 
most profound and laborious character, but before it was 
possible to explain these anomalous movements of Uranus, 
a problem of far greater difficulty remained to be solved, 
involving nothing less than a determination of the weight 
of the unknown planet, its distance from the sun, the 
nature of its orbit, and its position in the heavens at a 
particular time, indicating the region to which the tele- 
scope must be pointed to render visible what had hitherto 
remained for ages unseen by the eye of man. 

To those who have given but little attention to the 
study of these extraordinary problems an attempt to re- 
solve a question like that just presented may seem to be 
even presumptuous, yet when we come to examine the 
circumstances, we shall sec dimly a way whereby we may 
reach a certain approximate knowledge of the place of 
this unknown world. 

The fact that the planes of the orbits of all the more 
distant planets are nearly coincident with the ecliptic re- 
duced the examination to the great circle in the heavens 
cut out by the indefinite extension of this plane. This 



272 . NEPTUNE. 

is a most important consideration, and but for this fortu- 
nate circumstance no powers of research could ever have 
made even the most distant approximation to the place of 
the unknown planet. 

The empirical law of Bode, whereby it seemed that 
the order of distances of the planets was governed, as- 
signed to the hypothetical world a distance about double 
that of Uranus, or say, 3,600 millions of miles from the 
sun. Assuming this as the probable distance, the third 
of Kepler's laws would determine the period of revolution 
of the world whose position was sought. It remained 
now to assign a mass and position to the planet such as 
would render a satisfactory account of the perturbations 
of Uranus, which remained outstanding after the known 
causes of disturbance were exhausted. To accomplish 
this let us recall to mind the fact that in case the mean 
distance of the disturbing body had been rightly selected, 
then the interval between Uranus and the unknown, 
when in conjunction, would be about 1,800 millions of 
miles. In this position the disturbing force would exhi- 
bit its maximum power in a twofold sense : first, to 
cause Uranus to recede to its greatest distance from the 
sun ; and, second, to cause the same planet to lag behind 
the place it would otherwise have reached. In the 
above figure let U U' U" represent the computed orbit 
of Uranus, as existing under the combined influence of 
all known causes, P the place of the unknown, when in 
conjunction with Uranus at U'. It is manifest that the 
force exerted by P on Uranus will tend to accelerate its 
velocity in coming up to conjunction, and to cause the 
path described to lie outside the computed path along the 
dotted line, the planet really reaching the point U"', in- 



NEPTUNE. 



273 



Btead of U' in the undisturbed orbit. Leaving this point 
the force exerted by the unknown would reverse its 
effect, and a retardation would commence, and by slow 



IJ 



W 



u 



u 



i,-'"^ 



degrees receding from the disturbing body, it would 
gradually return to the undisturbed orbit, and there con- 
tinue until the period for the next conjunction might 
approach. 

Such is a rough exhibition of the reasoning which was 
employed to narrow the limits of research in the effort 
to point the telescope to the unknown cause of the per- 
turbations of Uranus. No account, of course, can be 
given of the mathematical treatment of the problem. It 
was undertaken at about the same time by Adams, of 
England, and by Le Verricr, of Paris. Each computer, 
unknown to the other, reached a result almost identical. 
Le Verrier communicated his solution to the Academy 
of Sciences on the 81st August, 1847, and on the even- 
ing of the 18th September, 1847, M. Galle, ol* Berlin 
directed the telescope to the point in which the French 
geometer declared the unknown planet would be found 

12* 



274 NEPTUNE. 

A star of the eighth magnitude appeared in the field of 
view, whose place was not laid down on any known 
chart. Suspicion was at once aroused that this might 
possibly be the planet of computation, and yet it seemed 
incredible that a problem far surpassing in difficulty any 
which had ever been attempted by human genius should 
thus at the first effort have been solved with such mar- 
velous precision. 

The suspected star was examined with the deepest in- 
terest in the hope that it might exhibit a planetary disk. 
In this, however, the astronomer was unsuccessful, and 
there remained but one method by which its planetary 
character might be determined, that of watching suf- 
ficiently long to detect its motion. This process, how- 
ever, must have tried very sorely the patience of the ob- 
server, as the motion of the planet at so great a dis- 
tance as three thousand six hundred millions of miles, 
was so slow as to require three entire months to pass 
over a space equal to the apparent diameter of the 
moon. The position of the suspected star having been 
accurately determined on the first night of observation, 
it became evident on the next night that the star had 
moved by an amount such as was fairly due to the slow 
motion of so vast an orbit. It could be none other than 
the unknown planet ! A success almost infinitely beyond 
the expectations of the most sanguine computer had 
crowned this mighty effort, and the amazing intelligence 
that the planet was found startled the astronomical 
world. 

The planet was soon recognized by the astronomers in 
every part of the world. The elements assigned by Le 
Yerrier and Adams by computation were accepted every- 
where with most unhesitating faith in their accuracy, and 



NEPTUNE. 275 

it was believed that it only remained for the telescope to 
verify the computations of these most wonderful mathe- 
maticians. In this the astronomical world were destined 
to meet a most remarkable disappointment. The new 
planet proved, indeed, adequate to account for all the 
anomalous movements of Uranus, while in all its ele- 
ments it differed so widely from those of the computed 
hypothetical planet that the computed and real planet 
could not in any way be regarded as the same body. 
The first restriction proved to be correct, for the orbit of 
the new planet (afterwards named Neptune) did coincide 
almost exactly with the plane of the ecliptic. The second 
restriction, based on the extension of Bode's law of in- 
terplanetary spaces, was falsified in the event, for here 
the law of Bode failed, and the distance of the true 
planet was nearly 5,000 millions of miles less than that 
of the computed one. 

The third restriction due to the application of Kepler's 
third law is verified in the real planet ; but as the dis- 
tance of the unknown was assumed greatly too large, of 
course the periodic time depending on this distance was 
also too large. This by necessity involved an error in 
the mass assumed for the unknown, whose erroneous dis- 
tance demanded, of eourse, an erroneous mass greater than 
that of the true planet; and yet, notwithstanding the 
magnitude of the errors of these elements, the computers 
succeeded in pointing the telescope within less than one 
degree of the actual place of die body which had caused 
the anomalous movements of Uranus ! 

We will endeavor to render a brief account of this 
most astonishing fact. It is evident that the disturbing 
effects of Neptune will become most powerful when the 
disturbing planet is nearest the disturbed one, or. what 



276 NEPTUNE. 

amounts to the same thing, the maximum disturbance 
will occur when the planets are in conjunction. We 
know that the periodic time of Uranus is 82 years, the 
periodic time of Neptune is 164 years, and hence it is 
easy to compute the interval from one conjunction to the 
next, which is no less than 171 years. The two planets 
passed their conjunction in 1822, and therefore the pre- 
vious conjunction must have occurred 171 years before, or 
in 1651 ; but the earliest recorded observation of Uranus 
was not made till 1690, or nearly 40 years after the 
conjunction, and at a time when the disturbing force of 
Neptune was so much diminished as to be nearly, if not 
quite insensible, for a long while. The minute disturbing 
power of Neptune still existing in 1690, would go on 
decreasing until, in 1782, the planets would be in oppo- 
sition, and would be separated by a maximum interval. 
After this date the distance between the planets would 
slowly decrease as they approached their conjunction, 
and in 1781, when Uranus was discovered, a small dis- 
turbing effect would begin to be appreciable, which would 
go on increasing up to the time of conjunction in 1822. 
Thus we perceive that mathematicians found the planet 
Uranus in such condition that the perturbing effects of 
Neptune were increasing in intensity from year to year ; 
and hence no set of elements could correctly represent 
the places of Uranus, because the observations did not 
extend back far enough to embrace the disturbed places 
of the planet at the former conjunction in 1651. No cor- 
rect solution was then possible until the perturbations 
should reach their maximum value, which occurred in 
1822, when the planets were in conjunction, and subse- 
quent to which period the planet Uranus would slowly 
return to its computed orbit as it receded further and 



NEPTUNE. 



277 



still further from the influence of the disturbing body, as 
may be more clearly seen from the figure below, in which 
the smaller circle may represent the orbit of Uranus, the 
larger one the orbit of Neptune. For a long while prior 




to conjunction in 1822, Uranus would be slowly over- 
taking Neptune, during which time the direction of the 
disturbing force would be such as to accelerate the orbital 
motion of Uranus, and to increase its distance from the 
sun. The acceleration would cease at conjunction, and 
would there be changed into equal and opposite retarda- 
tion, as is manifest from the figure, while the increase of 
the distance of Uranus must continue to increase even 
after conjunction, but the disturbing force must rapidly 
decline in power as the interval between the planets in- 
creases. Thus the great problem demanded the position 
of a disturbing planet at a , given time, which could ac- 
count for the known perturbations, all of which were 



278 NEPTUNE. 

crowded into a few years, say 25, before and after the 
conjunction in 1822. While this narrowing of the limits 
of sensible perturbation increased the chances of direct- 
ing the telescope to the unknown disturber, it seems to 
have really increased the difficulty of assigning to this 
disturber his exact orbit. Indeed, even with circular 
orbits, several might have been chosen, such that by vary- 
ing the mass of the unknown the perturbations might 
have been tolerably well represented, but in case ellip- 
tical orbits are chosen, then our limits are much extended, 
and the mean distance may be made to vary within very 
broad limits, provided the eccentricity may be chosen at 
pleasure. Thus the ellipse shown in the figure coincides 
between N and N' very nearly with the circular orbit, 
and in case a planet revolving in the circle could account 
for the anomalies of Uranus, the same would be tolerably 
well represented by the effects of a planet with a very 
different period and mean distance revolving in the ellip- 
tic orbit. Now this was exactly the case as developed in 
the final history of this grand discovery. The great geo- 
meters chose an elliptic orbit of such eccentricity and 
having its major axis in such position that the computed 
and true orbits agreed with each other in a most remark- 
able manner during the twenty years before and after 
conjunction. Their efforts were thus crowned with the 
success which they so eminently deserved ; and although 
the computed orbit came finally to differ greatly from the 
true one, yet, for the time when the computed orbit was 
required to represent the places of the unknown, and to 
point the telescope to its actual location, the computed 
orbit responded nearly as perfectly as the true one could 
have done, even had it been then known. 

It has been already stated that after the discovery of 



NEPTUNE. 279 

Uranus, when the elements of its orbit had been obtained 
with sufficient accuracy to render it possible to trace the 
planet backwards among the fixed stars, it was ascertained 
that it had been observed and its place recorded as early 
as 1690, and had been seen many times subsequently and 
prior to its discovery, being always mistaken for a fixed 
star, so we find in the case of Neptune, a like examina- 
tion by Professor Walker led to the discovery that the 
new planet had been twice recorded in position by La 
Lande, in May, 1795. These two observations were 
found to be outside the path which had been assigned the 
planet by the theory of both Le Verrier and Adams ; and 
such was the deep confidence in the accuracy of the ele- 
ments assigned by these two geometers that it was with 
great difficulty that some of the ablest astronomers could 
be induced to believe that the missing star twice observed 
by La Lande could be the new planet. The identity was, 
however, soon demonstrated, and hence arose the discus- 
sion which led to the declaration by an eminent mathe- 
matician that the discovery of Neptune was the result of 
a happy accident ; but we have seen that the grand pro- 
blem propounded by both the French and English astrono- 
mer, and which each resolved with such astonishing pre- 
cision, was to point the telescope in the direction of the 
unknown, which had produced the late excessive pertur- 
bations of Uranus. It remains, so far as I know, yet to 
be decided whether the data in possession of Adams and 
Le Verrier can be so treated by analysis as to give an 
orbit to the unknown more nearly agreeing with that of 
the known planet, 
Neptune's satellite.— The vast distance to which 

Neptune is buried in space will perhaps render it impos- 
sible to learn how many satellites revolve about this re- 



280 NEPTUNE. 

mote primary. The great refractors have certainly dis- 
covered the existence of one satellite, and another is 
suspected. The discovery of this one satellite of Neptune 
becomes, under all the circumstances, a matter of deep 
interest, as it enables us to determine the mass or weight 
of the primary, a matter of the first moment in comput- 
ing the effects of the planet as a disturbing body. The 
satellite is found to perform its revolution about the 
primary in a period of about five days and twenty-one 
hours, and at a mean distance of 232 thousand miles, or 
nearly equal to the distance of our moon from the earth. 
In case these distances are assumed to be exactly equal, 
then as at the same distance the centrifugal force in- 
creases as the square of the velocity, and as the velocity 
of Neptune's moon is about four and a half times greater 
than that of our moon, its centrifugal force in its orbit must 
be 4.5 x4.5, equal to about twenty times the centrifugal 
force of the moon. Now, the attractive force of Nep- 
tune is exactly proportioned to its weight or mass, and 
hence, to counterbalance this centrifugal force in his satel- 
lite, which is twenty times as great as that of the moon, 
the mass of Neptune must be twenty times as great as 
that of the earth. Thus has been revealed not one 
world, but two — the one containing a mass of matter 
sufficient to form no less than twenty worlds as heavy as 
our earth— the other a satellite, indeed, of the first, yet 
sufficiently large to send back to us, at a distance of 
3,000 millions of miles, the light of the sun, enfeebled 
by its dispersion over this vast distance to the one- 
thousandth part of the intensity it pours on our earth. 
We have reached the known boundary of that mighty 
confederation of revolving orbs which, whilst they ac- 
knowledge in the most specific manner a mutual depend- 



NEPTUNE. 281 

ence, are all controlled by the predominating influence 
of the sun, which occupies the common focus of all their 
orbits, and around which the jail roll and shine in obedi- 
ence to the grand law of universal gravitation. 

We shall now retrace our steps toward the sun, and 
consider a remarkable class of bodies, which for ages were 
regarded as evanescent meteors, suddenly blazing athwart 
the sky, and as suddenly fading from the vision, never 
more to reappear. Modern science has given to these 
bodies determinate orbits, and in some instances, as we 
shall see, has assigned them a permanent place among the 
satellites of the sun. 



CHAPTER XIV. 

THE COMETS. 

Objects of Dread in the Early Ages. — Comets Obey the Law of Gravi- 
tation and Revolve in some one of the Conio Sections. — Character- 
istics of these Curves. — Comet of 1680 Studied by Newton. — Comet of 
1682 named " Halley's Comet." — Its History. — Its Return Predicted. 
Perihelion Passage Computed.— Passes its Perihelion 13th April, 
1759. — Elements of its Orbit. — Physical Constitution. — Nucleus. — En- 
velopes. — Tail. — Intense Heat Suffered by some Comets in Perihelio. 
— Dissipation of the Cometic Matter.— Encke's Comet. — A Resisting 
Medium. — Deductions from Observation.— Biela's Comet.— Divided. — 
Number of Comets. 

In all ages of the world these anomalous objects have 
excited the deepest interest, not only among philosophers, 
but among all classes of men. The suddenness with 
which they sometimes blaze in the sky, the vast dimen- 
sions of their fiery trains, the exceeding swiftness with 
which they pursue their journey among the stars, the 
rapid disappearance of even the grandest of these seeming 
chaotic worlds, have all combined to invest these bodies 
with a power to excite a kind of superstitious terror which 
even the exact revelations of science cannot wholly dis- 
pel. History records the appearance of these phenomena, 
and in general they were regarded as omens of some 
terrible scourge to mankind, the precursors of war or 
pestilence or famine, or at the very least announcing the 
death of some prince or potentate. Some of the ancients, 
of course, rose above these superstitious ideas, and the 



THE COMETS. 283 

Roman philosopher Seneca even entertained the opinion 
that these erratic bodies would some day fall within the 
domain of human knowledge, that their paths among the 
stars would eventually be traced, and that they would be 
found in the end to be permanent members of the solar 
system. How remarkably this prediction has been veri- 
fied will appear in the concise sketch we are about to 
present. 

The discovery of the law of universal gravitation was 
followed by a mathematical demonstration, also accom- 
plished by the great English philosopher, which was the 
reverse of the problem he had just solved, and may be 
announced as follows : Given, the intensity of a fixed 
central force, decreasing in power as the squares of 
the distances increase, and the direction and intensity 
of an impulsive force operating to set in motion a 
body subject to the central power : Required, the na- 
ture and figure of the path described by the revolving 
body ? 

Previous to the resolution of this problem Newton 
naturally expected to find the curve sought to be an 
ellipse. The sun was the source of a fixed central force 
which obeyed the above law. The planets were retained 
in their orbits by this central force. These described 
ellipses in their revolution around the sun, and it was 
natural to conclude that the solution of the inverse pro- 
blem would lead to the elliptic orbit. On completing the 
solution and reaching tho mathematical expression repre- 
senting the orbit, it was found not to be the usual ex- 
pression for the ellipse, and after careful examination 
proved to be the general expression, embracing within its 
grasp no less than/owr curves, the circle, the ellipse, the 
parabola, and the hyperbola. These curves are allied in 



284 



THE C OMETS. 



a most remarkable manner, having certain properties in 
common, and having in one sense a common origin. 
They may all be obtained by cutting the surface of a cone 
by a plane passing in different directions, as may be seen 
from the figure below. Let A be the vertex, and CDE 




L the circular base of a cone seen obliquely. Any plane 
passed parallel to the base, or perpendicular to the axis 
A B, will cut from the surface a circle, asFEG. A 
plane passed obliquely to the axis will cut from the sur- 
face an ellipse, as M 0'. Any plane passed parallel 
to the side of the cone A C will cut the curve T W X, 
called a parabola, and any plane passed parallel to the 



THE COMETS. 285 

axis of the cone A B will cut out from the surface the 
curve K I L, called an hyperbola. These curves are 
thus all derived from the conic surface by intersecting 
it with a plane, and are hence called conic sections. 
JNTow, a little examination will show us that while the 
circle and ellipse are re-entering curves of limited ex- 
tent, this is not the case with the parabola and hyper- 
bola. If the conic surface were indefinitely extended 
below the base, it is evident that the cutting plane X W T, 
being parallel to the side A C, could never cut that par- 
ticular line, and hence the parabola, departing from the 
point U, and passing through T and X, would extend in- 
definitely on the surface of the cone without ever coming 
together, though the curves would approach each other 
for ever. Thus the parabola is the limit of all possible 
ellipses ; for it is manifest that as the cutting plane 
becomes more and more nearly parallel to the side 
A C, the axis of the ellipse cut out grows longer and 
longer, and just at the point where parallelism is reached 
the parabola is formed, and it is only an ellipse with an 
infinitely elongated axis. 

While it is seen that the branches of the parabola ap- 
proach each other, and may be said to come together at 
an infinite distance from the vertex at W, this is not the 
case with the branches of the hyperbola. Departing from 
the vertex I, and passing the points K and L, the 
branches of the hyperbola recede from each other for 
ever, losing by slow degrees their curvature, until at an 
infinite distance the curves degenerate into straight lines, 
and thus continue to recede for ever. Such are seme of 
the general characteristics of these remarkable curves. 
They all, like the ellipse, have a major axis, on each 
side of which they are symmetrical. They all have at 



286 THE COMETS. 

least one focus, possessing special properties. They all 
have a vertex lying at the extremity of the major axis 
and the nearest point of the curve to the focus ; and, 
strange as it may seem, in either one of these curves 
mathematical analysis demonstrated that a satellite of 
the sun might revolve under the law of universal gravita- 
tion. The elliptic orbits of the planets and the circular 
orbits of some of the satellites of Jupiter presented 
examples in the heavens of two of these curves, and it oc- 
curred to the sagacious mind of Newton that the hitherto 
unexplained eccentricity of the cometary revolutions 
might be accounted for by finding that they revolved 
around the sun in ellipses of great eccentricity, or pos- 
sibly in parabolic, or even in hyperbolic orbits. The 
English astronomer had the opportunity of putting to 
the test this grand idea by the appearance of a great 
comet in 1680, which displayed a train of light of won- 
derful dimensions and seemed to plunge nearly vertically 
downwards from the pole of the ecliptic, made its peri-' 
helion passage with almost incredible velocity, and with 
a speed always diminishing as it receded from the sun 
again swept out into the unfathomable depths of space. 
To this comet Newton first attempted to apply the law 
of gravitation, and to assign it an orbit among the conic 
sections. This could be done in the same manner from 
observation as in the case of a planet. Having obtained 
as many places of the comet as possible among the fixed 
stars, it remained to see whether any elliptic orbit or 
any parabolic orbit could be assigned the comet which 
would at the same time pass through all these observed 
places. If this could be done, then it would become pos- 
sible from this known orbit to predict the places of a 
comet as of a planet, and in the event of the orbit prov- 



THE COMETS. 287 

ing elliptic, then the return of the comet to its perihelion 
might be computed and announced. 

The comet of 1680 was carefully studied by Newton, 
and its orbit was found to be an extremely elongated 
ellipse, approaching very nearly to the form of a para- 
bola, but while its physical features and its near approach 
to the sun made it an object of extraordinary interest, the 
exceeding velocity with which it swept around the sun 
rendered it difficult to execute exact observations, and 
hence this comet was not well adapted to demonstrate the 
truth of the rigorous application of the law of gravitation 
to the orbital movements of these eccentric bodies. 
Another great comet appeared two years later, in 1682, 
to whose history there attaches a special interest, on 
account of the fact that it was the first of these bodies 
shown to have a permanent orbit in connection with the 
solar system, and the first whose periodic time was 
sufficiently well computed to render it possible to predict 
its return. This comet bears the name of the great 
English astronomer Halley, to whom we are indebted for 
the computation of the elements of its orbit — a problem, 
at the time it was executed, far more difficult than any 
belonging to the whole range of physical astronomy. 

The elements of the orbit of a comet are nearly iden- 
tical with those which fix the magnitude and position of a 
planetary orbit. To obtain the magnitude of the comet- 
ary ellipse we must have two elements, the length of the 
major axis and the perihelion distance. To obtain the 
direction of the longer axis we must have the position of 
the perihelion point ; this point, being joined to the sun's 
center, gives the direction of the major axis. To obtain 
the position of the piano of the orbit we must have the 
place of the ascending or descending node, and also the 



288 THE COMETS. 

inclination of the plane of the conietary orbit to that of 
the ecliptic. If, in addition to these elements, we have 
the time of perihelion passage, then it becomes possible 
to follow the comet in its erratic movements with a cer- 
tainty almost as great as that with which the orderly 
movements of the planets are pursued. 

On the appearance of the great comet of 1682, Halley 
undertook the laborious and hitherto unaccomplished task 
of computing rigorously the elements of its orbit, which 
task he accomplished after incredible labor in the most 
masterly manner. It then occurred to him to gather up 
all historic details with reference to the appearance of 
comets, as well as all astronomical observations, so that 
by examination and inter-comparison he might learn 
whether any recorded comet had ever pursued the same 
track in the heavens which had just been passed over by 
the comet of 1682. In the course of this historical in- 
vestigation he found that comets, somewhat resembling in 
physical appearance, and traversing nearly the same 
regions of space passed over by his own comet, had ap- 
peared in the years 1531 and 1607, and now again in 
1682. These epochs are separated by an interval of 
between seventy-five and seventy-six years, and Halley, 
after long and laborious computation, announced that in 
1759, three quarters of a century from the date of the 
prediction, this same comet would again return to our 
system ! We can readily sympathize with the feelings 
of this great astronomer when we find him appealing to 
posterity to remember, in the event of his prediction being 
verified, that such an occurrence as the return of a comet 
was first announced by an Englishman. As the year 
1759 approached, the prophetic declaration of Halley ex- 
cited an unusual interest throughout the astronomical 



THE COMETS. 289 

world. To predict the exact point in the heavens to 
which the telescope must be directed to catch the first 
faint glimpse of the returning stranger, and to give the 
date of its perihelion passage, required investigations of 
so high an order, that in case they had been demanded of 
Halley, seventy-six years before, the then existing con- 
dition of mathematical and physical science would not 
have furnished the means for their accomplishment. 
The whole subject of planetary perturbations had by this 
time been tolerably well developed, and the laborious 
task of computing the disturbing influence of Jupiter and 
Saturn was undertaken by Clairault, assisted by La 
Lande and by a lady, Madam Lepaute, whose name stands 
in honorable union with the two profound mathematicians. 
After many months of indefatigable labor the computers 
announced that for want of time they had been compelled 
to omit several matters which might make a difference 
of thirty days, one way or the other, in the return of the 
comet, but that within these limits this long lost celestial 
wanderer would pass his perihelion on the 1 3th April, 
1759. The limits of error were justly chosen, for the 
comet actually returned and passed its perihelion on the 
12th of March, just a month ahead of tho predicted time. 
This successful computation settled for ever the doc- 
trine of the comctary orbits, and demonstrated beyond 
doubt their subjection to the attractive power of the sun, 
and that this orb extended its influence into the profound 
depths of space, to which tho comet descended during its 
journey of seventy-six years. It was further established 
that Ilalley's comet was a permanent member of the 
solar system, performing its orbital revolution around the 
sun in an exceedingly elongated ellipse, but with a regu- 
larity equal to that of the planets. It was further de- 
li? 



290 THE COMETS. 

termined that the entire mass of the comet was very in- 
considerable, as no account of this mass was made in the 
computations for perturbation, while the masses of Jupi- 
ter and Saturn required to be known with precision. 
This comet has returned a second time since its discovery 
by Halley, when its elements were more accurately ob- 
tained by many modern astronomers, and perhaps best of 
all by Hermann Westphalen, who predicted its peri- 
helion passage, after an absence of seventy-six years, to 
within Jive days ! This appearance took place at the 
close of 1835. We shall have occasion to recur to this 
comet again when we come to speak of their physical 
constitution. 

Westphalen furnishes the following as the actual di- 
mensions of Halley' s comet 



Perihelion distance, . 
Aphelion " 
Length of the major axis, 
Breadth of the orbit, . 



55,900,000 miles. 
3,370,300,000 " 
3,426,200,000 " 
826,900,000 " 



It is thus seen that in its journey from the sun this 
comet crosses the orbits of all the known planets, and 
passes the boundary of Neptune more than three hundred 
millions of miles. 

Having thus demonstrated the subordination of these 
extraordinary bodies to the law of universal gravitation 
and to the received laws of motion, we will proceed to 
examine their 

Physical constitution. — The solid earth we in- 
habit, the moon, her satellite, the sun and all the planets, 
are compact masses of matter of differing densities, but 
of firm, compact materials. The comets, on the contrary, 
as a class, seem to be vaporous masses, far more unsub- 
stantial than the lightest summer cloud, and in general 



THE COMETS. 291 

transparent, or at least translucent, even in their most con- 
densed portions. This is evident from the fact that the 
minute stars are still visible with undiminished light 
when seen sometimes through a depth of cometary mat- 
ter millions of miles in extent. Comets in general con- 
sist of a nucleus or head, the center of force and the most 
condensed portion of their matter. Around this head 
there is seen usually a vaporous envelope or atmosphere 
of greater or less extent, sometimes evidently divided 
into concentric layers of nearly globular form. Many 
comets, on approaching the sun, undergo extraordinary 
physical changes in the head or nucleus, which experi- 
ences an excessive agjitation, flinging out jets or streams 
of fiery light in a direction towards the sun, which as- 
sume many and strange forms, sometimes spreading out 
into a fan-shaped figure, and rapidly fading in intensity, 
as they recede from the nucleus. This phenomenon is al- 
most invariably attended or followed with another even 
more remarkable — the throwing off a train of luminous 
matter, called the tail, in a direction opposite the sun, 
and sometimes extending to a prodigious distance. Thus 
the tail of the great comet of 1680, already mentioned, 
according to the computations of Sir Isaac Newton, 
reached to a distance of more than 140 millions of miles, 
while only two days were occupied in projecting this in- 
scrutable and mysterious appendage to this enormous dis- 
tance. The form of the tail is usually that of a hollow 
paraboloid, the nucleus occupying the focus, and thus 
the tail, as it recedes from the head, seems to diverge 
into two streams of light, while the axis or central lino is 
comparatively dark. Sometimes, as in the great comet 
of 1858, the region immediately behind the nucleus "on 
the axis is jet black — the intensity oi' this blackness 



292 THE COMETS. 

growing less arid less along the axis until it finally fades 
out in the general luminosity of the tail. 

The nucleus is sometimes tolerably well defined, and 
presents a planetary disk of greater or less magnitude. 
It is not intended to assert that there are no comets which 
are solid bodies, at least in some portion of their central 
masses. Indeed, if we are to credit the records, some 
have been seen in the act of crossing the disk of the sun, 
when they have appeared as round, well defined, circu- 
lar black spots, exactly like the planets Venus and Mer- 
cury, when seen in the same condition on the bright sur- 
face of the sun. For the most part, however, we know 
that these bodies do not present any evidence of solidity. 
Their heads or nuclei are ill defined when examined by 
powerful telescopes, and their gaseous condition is demon- 
strated by the fact that they expand and contract their 
dimensions with great rapidity, according to circum- 
stances. 

This contraction generally takes place as the comet ap- 
proaches its perihelion passage, which is certainly a very 
curious fact, and quite contrary to what we would expect, 
as the excessive heat to which a comet must be subjected 
in perihelio ought (as would seem) to greatly expand its 
dimensions. It is doubtless owing to the fact that this 
enormous heat extends its influence so far that the vapor- 
ous mass is expanded and rarified to such a degree as to 
become absolutely transparent and invisible, and it is only 
when released from this intense heat by recess from the 
sun that a condensation takes place, and thus the seem- 
ing dimensions of the comet increases. It is difficult to 
comprehend how some of these bodies, in their nearest ap- 
proach to the sun, are not absolutely burned up and dis- 
sipated for ever. The great comet of 1680, when in 



THE COMETS. 293 

perihelio, was only about 147,000 miles distant from the 
sun's surface; and admitting that the heat of the sun 
diminishes as the square of the distance increases, Newton 
computed that the comet was subjected to a heat 2,000 
times more intense than that of red hot iron. The great 
comet of 1843 is computed to have approached the sun's 
surface to within half the above distance, and Sir John 
Herschel computes that the intensity of the heat then ex- 
perienced by this comet was 47,000 times greater than 
the h^at of the sun as received at the earth, or more than 
twenty-eight times greater than the heat concentrated at 
the focus of a lens of thirty-two inches diameter, which 
melted agate and rock crystal, and dissipated these re- 
fractory solids into an invisible gas ! 

After passing under the influence of such intense heat, 
it seems almost impossible that any well defined form 
should ever be recovered, and yet the comet of 1680 and 
that of 1843 finally receded from the sun, the nucleus 
in some mysterious way slowly gathering up its dis- 
persed particles and sweeping away into the depths of 
space, a well-defined luminous object, not in any sensible 
degree injured in its form or magnitude by this fiery 
ordeal. 

The envelopes of comets and their tails are by far the 
most inscrutable problems of nature. Of these pheno- 
mena no satisfactory account has yet been rendered. 
The envelopes of the comet of 1858 were beautiful in 
form, with a well defined circular outline, in whose center 
the nucleus blazed with its fiery light. The diameter o( 
this seemingly globular mass changed from night tonight. 
Its texture varied ; sometimes evenly and beautifully 
shaded and gauze-like in its surface, and sometimes this 
gauzy surface broken by dark and irregular patches. .V 



294 THE COMETS. 

second concentric sphere became visible, fainter in its 
outline than the interior one, and finally a third circle 
dimly presented its outline, very faint, and only to be 
seen in powerful telescopes, under favorable circum- 
stances. 

The beautiful forms exhibited in these envelopes and 
retained by them seems to demonstrate the existence of 
some central repulsive force located in the nucleus, and 
capable of holding these gaseous particles in equilibrium. 
What this force may be it is vain to conjecture. If the 
envelope of the nucleus is a phenomenon surpassing the 
reach of human thought, what shall we say of the still 
more mysterious and incomprehensible phenomena pre- 
sented in the tails of comets ? 

VTe have already said that these tails are thrown off in 
a direction opposite the sun as the comet approaches its 
perihelion passage. As the comet sweeps around the sun 
with almost inconceivable velocity, the tail retains its di- 
rection, just as though its axis were a solid bar of iron, 
passing through the nucleus to the sun and hanging on 
the center of the solar orb. This bar, extending out to 
the furthest extremity of the tail 3 sometimes 120 millions 
of miles beyond the nucleus, sweeps round angularly with 
equal rapidity at every point, so that its rectilinear figure 
is preserved in this tremendous sweep. In case the tail 
were composed of ponderable particles, obedient to the 
laws of gravitation and motion, this would be impossible, 
for if we consider each particle an independent body, de- 
scribing an elliptic or parabolic orbit about the sun, 
the laws of their motion would compel the more distant 
particles to lag behind the nearer ones in angular 
velocity. 

If no comet ever exhibited any other than this peculiar 




THE GREAT COMET OF 1858. 
KNOWN AS DONATIS COMET 



THE COMETS. 295 

form of tail, straight and directed from the sun, we 
might frame atn hypothesis which could account for the 
facts; hut in some instances there are many tails to the 
one nucleus, and these not straight, but curved like a 
cimetar. In other cases there are two tails, the one, as 
usual, directed from the sun, the other pointing towards 
the source of light. Sometimes the principal tail is 
straight, and in the direction from the sun, while a lateral 
ray shooting from the nucleus may form with the axis of 
the tail an angle of thirty or even sixty degrees. 

We have already said that the tail swings around the 
sun in the perihelion passage, preserving its form and di- 
rection, and hence, when the comet is receding from the 
sun, the tail, in all its vast dimensions, is driven before 
the head of the comet, preceding the nucleus as it sweeps 
outward into space. 

In some instances corruscations have been noticed to 
take place in these grand but mysterious appendages, 
darting with incredible velocity from the very nucleus to 
the extremity of the tail, and thus flashing backwards 
and forwards like a magnificent auroral display. 

The question arises, What are these luminous dis- 
plays ? Are the tails of comets composed of ponderable 
matter ? If so, do they yield obedience to the known 
laws of motion and gravitation ? Is there any matter in 
the universe which may ever become luminous, but is im- 
ponderable ? Can these tails be a mere effect produced 
on the waves of light emitted by the sun in passing 
through the mass of cometary matter? These and many 
other questions equally difficult present themselves in 
this connection. The re-absorption of the tail into the 
head would seem to demonstrate that the matter compos- 
ing the tail was ponderable, while the facts already stated 



296 THE COMETS. 

as to the rigid form preserved by the tail in sweeping 
around the sun positively contradicts this hypothesis. 

One thing we know : cometary matter is ponderable 
matter, and obeys the laws of motion and gravitation, is 
swayed by the sun and by the planets, and in all par- 
ticulars complies with the laws governing other ponder- 
able matter. This we know, because, as we have seen, 
it is possible to predict the return of a comet revolving 
even in so great a period as seventy-five years, and such 
predictions have been rigorously verified. In case any 
portion of this ponderable matter were absorbed in the 
sun ; or dissipated by the intense heat which it suffers in 
the perihelion passage, then would the mass of the comet 
grow less at each return, and the periodic time would 
slowly diminish. There is one comet, named after its 
illustrious discoverer, Encke, whose history for the past 
thirty years has been followed with high interest, be- 
cause it is now a fixed truth that at each return its peri- 
helion passage is accelerated by about two and a half 
hours. It revolves in an elliptical orbit of small dimen- 
sions comparatively, a*nd performs its revolution around 
the sun in a period of only 1,205 days, or about three 
and a third years. By assuming the existence of a rare 
insisting medium. Professor Encke has succeeded in ac- 
counting for the acceleration in the motion of these 
comets, and this hypothesis has been generally received. 
In case its truth becomes established it involves remote 
consequences from which the mind naturally revolts ; for 
if there be a medium capable of destroying any portion 
of the velocity of Encke's comet, the same resistance 
must in like manner destroy a part of the orbital velocity 
of every planet and satellite, and sooner or later each in 
its turn must by sIoav degrees approach the sun, and in 



THE COMETS. 297 

the end this grand central orb must become the grave 
of every planet and satellite and comet ! Such an hypo- 
thesis is combatted, possibly disproved, by the fact that 
its influence has not yet been discovered on any one of 
the planets or on any satellite. It may be argued that 
on these solid substantial bodies it would require ages to 
produce sensible effect, while on the vaporous ethereal 
mass of Encke's comet even an almost evanescent medium 
might produce a sensible effect, even in a single revolu- 
tion of 1,205 days. May it not be possible to account 
for the decrease of the periodic time of Encke's comet 
without having resort to an hypothesis involving the 
destruction of the entire universe ? In case we admit 
that it loses a portion of its ponderable matter at each 
perihelion passage, then there must result an effect like 
the one observed, the comet slowly approaching the sun, 
to be dissipated entirely, however, before absolutely fall- 
ing on the surface of the central orb. 

However, it is useless to speculate. The facts now 
in our possession are not sufficient to enable us to render 
a satisfactory account of the various phenomena in the 
physical constitution of these bodies which have been 
enumerated, and we can only hope that the diligence 
and pertinacity with which this branch of astronomy is 
now pursued, may before long eventuate in removing 
from the science this only source of doubt and uncer- 
tainty. 

In the meanwhile the conclusions reached by Sir John 
Herschel, from an extended and careful observation oi' 
all the phenomena presented by llalley's comet in 1835, 
6, have been strengthened by the facts recorded both in 
Europe and America of the great comet of 1818. All 
the observations go to demonstrate — 



298 THE COMETS. 

1. That the surface of the nucleus nearest the sun 
becomes powerfully agitated, and finally bursts forth into 
luminous jets of gaseous matter. 

2. That this matter, with an initial velocity driving it 
towards the sun, is by some unknown repelling force 
driven backwards from the sun, and drifted outward from 
the sun to vast distances forming the tail. 

3. That a portion of this vaporized material is not 
subject to this repulsive force, but remains under the in- 
fluence of some equally inscrutable central power lodged 
in the center of the nucleus, and forming the corona or 
envelope, and assuming forms of great delicacy and 
beauty. 

4. That the force which ejects the tail cannot be gravi- 
tation, as it acts with a power and in a direction opposed 
to this central power. 

5. That the power lodged in the nucleus, and by whose 
energy the particles composing the tail are again re- 
absorbed into the head, cannot be gravitation, as the 
minute mass of the comet could not by its gravitating 
power bring back the particles flung off to such enormous 
distances. 

In this catalogue of inscrutable phenomena we must 
place the remarkable fact of the splitting up of a comet 
into two distinct portions. A comet of short period, known 
as Biela's comet, revolving in about six and three quarter 
years, was recognized as early as 1826, as a permanent 
member of the solar system. 

This comet, at its appearance in 1832, excited a pro- 
found sensation, in consequence of the prediction that it 
would c?'oss the earth s path, thereby creating the great- 
est alarm among the ignorant lest this crossing might 
occasion a collision between the comet and the earth. 



THE COMETS. 299 

The prediction was verified, but while the comet was in 
the act of crossing the earth's track or orbit, the earth 
was many millions of miles removed from this special 
point of intersection. 

The appearance in 1846 was again rendered memor- 
able by the strange phenomenon already mentioned — the 
actual severation of the comet into two bodies, distinct 
and separate, each cometary in its appearance, and each 
alternately preponderating in apparent magnitude and 
brilliancy. These two comets possessed all the charac- 
teristics which mark these anomalous bodies. Each had 
its nucleus, its envelope, and its tail. The first indica- 
tion of a separation occurred as early as the 19th Decem- 
ber, 1845. By the middle of January, 1846, the sepa- 
ration was complete, and was well observed in Europe 
and America. By the beginning of March the interval 
had increased to a maximum, when it was about one-third 
as great as the apparent diameter of the moon. From 
this time the companion comet began to fade, remaining 
faintly visible up to the 15th March. After this the old 
comet remained single, and finally disappeared. 

Here we have phenomena of the most extraordinary 
character. What convulsion could have split this nebu- 
lous mass into two distinct fragments ? What wonderful 
power could have occasioned the alternations in the in- 
tensity of their light ? What mysterious bond could 
have united these severed and separated bodies, and 
caused them to vibrate about their common center of 
gravity? Have these bodies been permanently re-united ? 
or will they ever appear as individual and independ- 
ent objects ? These questions it is now impossible to 
answer. 

The number of comets far exceeds that of the planets 



300 THE COMETS. 

and their satellites, and, indeed, judging from the list of 
recorded comets, and taking into account the fact that 
multitudes of these bodies must escape notice entirely by 
their remaining above the horizon in the day time, we are 
forced to the conclusion that they are not to be numbered 
by hundreds or thousands, but probably by millions ! 
They seem to obey no law as to the inclination of their 
orbits or the direction of their motions. Some appear 
to plunge vertically downwards from the very pole of the 
ecliptic, while others rise upward from below this plane 
in a direction diametrically opposite. Their planes are 
inclined under all angles, and their perihelion points are 
at all distances from the sun. Some revolve in orbits of 
moderate eccentricity, while others sweep away into 
space in parabolic or even in hyperbolic orbits, never 
again to visit our system unless arrested and diverted 
from their path by some disturbing power. The mighty 
depths to which some of these bodies penetrate into space, 
sweeping, as they must, vastly beyond the boundary of 
the planetary system, would excite a doubt in the mind 
as to whether there might be room enough in space 
for the undisturbed revolution of these wonderful ob- 
jects. We shall see hereafter that profound investiga- 
tions have answered this inquiry and dispelled every 
doubt as to the grandeur of the scale on which the uni- 
verse is built. 

In the Appendix will be found the elements of the 
orbits of such comets as are regarded permanent members 
of the solar system. 

We here close our examination of the various classes 
of attendants on the solar orb. We find this mighty sys- 
tem of revolving worlds composed of bodies which are 
diverse in their physical constitution, some more dense 



THE COMETS. 301 

and solid than the earth on which we dwell, some far 
more rare and unsubstantial than the atmosphere we 
breathe- — all obedient to the grand controlling power of 
the central orb, while no one is relieved from the dis- 
turbing influence of every other — a vast complicated 
display of celestial mechanism, whose equilibrium and 
stability presents the grandest problem for human in- 
vestigation to be found in the whole universe of matter. 



CHAPTER XV. 

THE SUN AND PLANETS AS PONDERABLE BODIES. 

General Circumstances of the System. — Tjte Sun.— His Diameter and 
Mass. — Gravity at the Surface. — Mercury. — His Mass and Perturba- 
tions. — Venus as a Ponderable Body.— Long Equation of Venus and 
the Earth. — The Earth and Moon as Heavy Bodies. — Figure and 
Mass op the Earth. — Precession. — Aberration. — Nutation. — Mars. — 
His Mass and Density.— Gravity at His Surface. — The Asteroids. — 
Jupiter's System, — Saturn. — His Moons and Eings as Ponderable 
Bodies. — Uranus. — Neptune. — Stability of the whole System. 

Having now completed a rapid survey of the bodies 
which owe allegiance to the sun, and having reached to 
a knowledge of those laws which extend their empire over 
all these revolving planets, we come to the considera- 
tion of the modifications which are introduced into the 
circumstances of motion of each of these worlds, by the 
fact that it is subjected to the influence of all the others. 
As under the great law of universal gravitation every 
particle of matter in the universe attracts every other 
particle of matter with a force which varies inversely as 
the square of the distance and directly as the mass, it 
follows that each planet and comet and satellite of the 
entire system of the sun are, to a greater or less degree, 
affected by the attraction of every other. 

We have already considered generally the great pro- 
blem of the " three bodies" — a central, a disturbing, and 
a disturbed body. The train of reasoning there presented 



PONDERABLE BODIES. 303 



is now to be carried out and extended in succession to the 
planets and their satellites. Before proceeding to ex- 
amine the changes wrought in the orbits of the planets 
and their satellites by the action of all the disturbing 
forces, we will make a more general examination of the 
various elements of the planetary orbits, to learn, if pos- 
sible, whether any of these elements are subjected to 
changes which are merely periodic in their character, re- 
turning after intervals, longer or shorter, to their normal 
condition, to repeat the same changes in the same order 
for ever. We desire also to inquire whether any of the 
elements are subjected to perturbations which always pro- 
gress in the same direction, and if so, whether these 
changes in any way involve the destruction of the system 
as such. 

This is undoubtedly the grandest problem ever pro- 
pounded to the human mind, for it is neither more nor 
less than an inquiry into the perpetuity of the great 
scheme of worlds dependent on the sun. It demands 
a vision which shall penetrate the future ages to pre- 
dict the mutations and their effects at the end of these 
ages. It will not be expected that in such a treatise as 
this we are to enter into an exhaustive discussion of this 
great subject. We can do little more than announce the 
results reached by the profound investigations of the great 
mathematical successors of Newton. 

We shall commence, then, by an inquiry touching 
those elements of an orbit which involve the well-being 
of a planet, or its fitness to sustain the animal and vege- 
table life which exists on its surface. 

The figure and magnitude of an orbit are determined 
by the length of the major axis and by the eccentricity, 
and in ease but one planet existed, these are the only 



304 THE SUN AND PLANETS 

elements whose value could in any way affect the physical 
condition of the planet, so far as its supply of light and 
heat received from the sun are concerned. In this case 
the position of the orbit in its own plane (determined by 
the place of the perihelion point) and also the position 
of the plane of the orbit, as referred to any fixed plane, 
(determined by the angle of inclination and line of 
nodes), and also the epoch (or place of the planet in its 
orbit at a given moment of time), all those quantities 
would not in any degree affect the actual condition of the 
planet ; but as no planet is isolated, and as each is sub- 
jected to the influence of every other, it becomes a mat- 
ter of grave importance to ascertain whether there be any 
fluctuations in the values of all these elements, whether 
these fluctuations are confined within any specific limits, 
and whether, if thus confined, any injurious effect can 
result to those elements which involve the well-being of 
any planet ; and finally, whether there be any guarantee 
for the perpetuity of the planetary system in the condi- 
tion now existent. 

In case the planes of the orbits of all the planets were 
coincident, then the investigations would be confined to 
the fluctuation in the values of the major axes, eccen- 
tricities and perihelia; but from the reasoning already 
presented in the problem of " the three bodies," we have 
seen that if we consider the relation of two planets whose 
orbits are inclined under any angle, in their reciprocal 
influence, if we assume the plane of the orbit of one of 
these planets, for example, the earth, as fixed in position, 
and the plane of the other planet's orbit (as Mars) as in- 
clined to this, under a given angle, it is clearly manifest 
that the disturbing influence of the earth on Mars will be 
reversed when Mars passes through the plane of the 



AS PONDERABLE BODIES. 305 

earth's orbit. Suppose we could place our eye in the 
prolongation of the line of intersection of the two orbits, 
then we should see them as two straight lines, inclined to 
each other, as in the figure below, in which S represents 



K 



the place of the sun, E E r places of the earth, and M and 
M' places of Mars. Now, when Mars and the earth are 
on the same side of the sun, or the line of nodes, Mars 
ascending towards M', above the plane of the earth's 
orbit, the force exerted by the earth on the ascending 
planet tends to draw it downward to the ecliptic, and 
hence it will not quite reach the elevation M', and thus 
all this while the plane of the orbit of Mars will be form- 
ing a less and less angle with the ecliptic. The moment, 
however, the planet reaches its highest elevation and 
commences to descend towards the ecliptic to pass its de- 
scending node, then the earth, remaining stationary, will 
pull the planet towards its own plane, and hence the de- 
scent will be made steeper, and the angle of inclination 
of the orbit of Mars will, while the planet thus descends, 
be always increasing. Following Mars below the plane 
of the ecliptic, the earth remaining as before, we see that 
here the tendency is to pull Mars up to the earth's orbit, 



306 THE SUN AND PLANETS 

and hence it will not quite reach the point M, or the in- 
clination in this descent below the ecliptic will diminish. 
From this point, as Mars begins to ascend, the earth's at- 
tractive energy will cause it to ascend more rapidly, and 
will make it pass its ascending node earlier than if un- 
disturbed, and as it comes up faster, it must ascend a 
steeper grade, or the inclination will increase. Thus we 
see that Mars, in ascending or descending to pass either 
node, will both ascend and descend by a steeper grade 
because of the earth's attraction, while in passing from 
either node to the highest and lowest points of its orbit 
the same force will operate to make the planet reach 
points less remote from the ecliptic than if undisturbed, 
and hence to ascend and descend with a smaller angle of 
inclination. Now, a careful inspection will show that the 
effects produced by the earth on Mars, while situated at 
E', will be greater in the half of the orbit of Mars which 
lies above the ecliptic, and at the end of one revolution an 
exact compensation may not be effected, so that the in- 
crease of the angle of inclination may not be exactly 
equal to the decrease. But as the earth is revolving, a 
time will come when this body will occupy the point E, 
and then the most powerful effect will be produced when 
Mars is below the ecliptic, and in case the orbits are 
circular, an exact symmetry existing, at the end of a cer- 
tain cycle the inclinations will be exactly restored. 

The fact that the orbits of the planets are elliptical in 
figure cannot in any way lessen the force of the reasoning 
we have employed ; it can only postpone to a more remote 
period the final restoration of the inclinations of the 
planetary orbits. Under the powerful and masterly 
analysis of Lagrange this subject was completely ex- 
hausted, and a result reached which in the following pro- 



AS PONDERABLE BODIES. 307 

position guarantees the stability of the inclinations through 
all ages :— 

" If the mass or weight of every planet be multiplied 
by the square root of its major axis, and this product be 
multiplied by the tangent of the angle of inclination of 
the plane of the planetary orbit to a fixed plane, and these 
products be added together, their sum will be constantly 
the same." 

Now, we will show hereafter that the major axes re- 
main nearly invariable, the masses of the planets are ab- 
solutely so, and hence the third factor of the product, the 
tangent of the inclination, can only vary within narrow 
limits, returning at the end of a vast cycle to the primi- 
tive value. 

We shall see hereafter how important the stability of 
the inclination of the earth's orbit is to the well-being 
of the living and sentient beings now on the earth's 
surface. 

We proceed to examine the changes of the lines of 
nodes due to perturbation. These changes are allied to 
those of inclination, and are, indeed, a necessary conse- 
quence of these changes, as may readily be shown. 




308 THE SUN AND PLANETS 

For this purpose we return to the figure already em- 
ployed, using the same planets, Mars and the earth, re- 
garding the movements of Mars to be disturbed by the 
earth's attraction. 

We have already seen that in case Mars be at M, the 
earth being at E, the planet, in descending its orbit to 
the line of nodes seen as in S, (the eye of the spectator 
being in the prolongation of the line of nodes) during the 
entire descent the planet will be drawn down to the plane 
of the ecliptic E E' on a steeper grade than the normal 
one M S, and hence the planet will pass through the 
ecliptic earlier than if undisturbed, or at a point which 
will be seen somewhere between S and E. Thus dur- 
ing this descent the node will go backwards to meet the 
planet, or will retrograde. Passing below the ecliptic, 
the planet continuing to descend, will, as we have seen, 
be prevented by the disturbing body from reaching a 
point so low as M', and hence if its path for a moment 
were anywhere produced backwards, this line would meet 
the ecliptic at some point always approaching E, or here 
again the line of nodes retrogrades. The same reasoning 

o o o 

will show that with the above configuration the retro- 
gradation of the line of nodes must continue with unequal 
velocity during the entire revolution of the planet. In 
other configurations there is sometimes an advance of the 
node, but in the long run it is easily demonstrated that 
the nodes of all the planetary orbits on any fixed plane 
will retrograde and perform entire revolutions in periods 
of greater or less duration. 

This perpetual recess of the lines of nodes in one direc- 
tion does not in any way affect the physical condition of 
a planet, but serves an admirable and necessary purpose 
in securing final stability in the planetary system by 



AS PONDERABLE BODIES. 309 

presenting the disturbed orbits to the disturbing bodies 
under all possible configurations. 

We shall not attempt to exhibit in full the reasoning 
by which the variations of the remaining elements are 
shown to be periodic, when periodicity is essential to 
stability, or progressive when progression does not in- 
volve destruction, but from a single figure deduce, if pos- 
sible, the great principles involved in this wonderful 
problem. 




Let S represent the sun, E the earth, and P any 
planet disturbed by the earth, and let us suppose that un- 
disturbed in any small portion of time it would reach l v , 
but subjected to the influence of the earth's attraction it 
reaches P" in the same time. The question is, in what 
way does this change affect the elements of P's orbit ? 

We have already seen the effect on the inclination and 
line of nodes. These elements do not affect the magni- 
tude of the orbit nor the position of that orbit in its own 
plane. The magnitude and position depend on the length 
of the major axis, eccentricity and perihelion point, Let 
us examine these in order, commencing with the length 
of the major axis. 



310 THE SUN AND PLANETS 

We suppose the planet P to be moving, when undis- 
turbed, with its normal elliptic velocity, and of course on 
reaching P', the longer axis of its orbit, and in fact all 
the elements remain unchanged in value ; but being dis- 
turbed, so as to be prevented from reaching P', and being 
compelled to reach P /; , will this compulsion merely 
change the position of the planetary orbit, or will it in- 
crease or decrease the length of the major axis? 

Kepler's third law tells us that the squares of the 
periodic times are proportional to the cubes of the major 
axes, and from this relation it is manifest that any change 
in the elliptic velocity of a planet must change the period 
of its revolution, and this involves a change by neces- 
sity in the major axis of the orbit. 

The question of change in the major axis, then, re- 
solves itself into an inquiry as to whether the disturbance 
has produced any change in the elliptic velocity of the 
disturbed planet. 

At the first glance it may seem impossible to drag a 
planet from its normal elliptic path without affecting its 
velocity. This, however, is not the fact. If a body be 
moving in a straight line and a force be applied to it 
perpendicular to the direction of its motion, this force 
will not in any degree affect the velocity, but only the 
direction of the moving body. Thus a ball fired from a 
rifle on the deck of a fixed or moving boat, with the same 
initial force, will reach the opposite shore in the same 
time, but its direction of absolute motion is changed if 
fired from a moving boat, from what it would be if shot 
from one at rest. So a flying planet may be subjected 
to the action of a force always perpendicular to the di- 
rection of its motion, which force may push it from its 
normal path, but cannot affect its elliptical velocity. 



AS PONDERABLE BODIE 



311 



Such a force, then, can have no influence on the length 
of the major axis, or on the periodic time of the re- 
volving body. 

Now, every force is capable of being changed into three 
other forces whose combined action will produce the same 
effect as the primitive force, as in the figure. 




Let P P"" represent the direction and intensity of any 
force ; on this line as a diagonal construct the solid 
figure a parallelopiped. Then the sides P P , P V and 
P Y" will represent the direction and intensity of three 
forces, which would produce the same effect as the force 
P P"". 

Precisely in this way the disturbing force exerted by 
the earth on the planet P can be converted into three 
other forces, whose combined effect shall be identical with 
the original force. Two of these forces shall lie in the 
plane of the planet's motion, the one tangent to the 
orbit, or in the exact direction of the planet's motion, 
the second perpendicular to the direct ion of motion, or 
normal to the orbit, and the third perpendicular to the 
plane of the orbit of the planet. 

Now, from what we have said, it is clear that but one 



312 THE SUN AND PLANETS 

of these new or substituted forces can in any way affect 
the velocity of the planet, and that is the force tangent 
to the orbit, or coincident with the direction in which it 
is moving. The normal component (as it is called) 
pushes the planet from its old orbit and the perpendicu- 
lar component pushes the planet above or below its own 
plane of motion, but neither of these affect the velocity 
of the moving planet, and neither of them can in any de- 
gree affect the length of the major axis. 

The perpendicular component has already been con- 
sidered in its effects, for it is this force which changes the 
inclination and gives motion to the line of nodes. We 
may, therefore, in our future examinations leave this 
force out of consideration, or, which comes to the same 
thing, consider the planes of the orbits of the disturbing 
and the disturbed planet as the same. 

Let us, then, represent by the two circles the orbits 
of the planets in question, S being the place of the sun, 



E the earth, and P the planet when in conjunction. In 
this configuration the entire disturbing power of E is 
exerted along the line E P, or perpendicular to the direc- 
tion of the planet's motion, or normal to its orbit, and in 



AS PONDERABLE BODIES. 313 

this position the tangential force being nothing, the major 
axis is undisturbed by E. As P moves towards P' the 
direction of the force exerted by E ceases to be normal to 
P's orbit, and may be replaced by a normal and a tan- 
gential force. The tangential force from P towards P' 
is manifestly in opposition to the motion of P in its orbit, 
and therefore retards its motion, and thus decreases its 
major axis ; but there is a point P" symmetrically placed 
with reference to P, where the tangential force is in the 
opposite direction, and in an equal degree becomes an 
accelerating force, and whatever the major axis might 
lose in length from the disturbing power at P', it would 
gain from the same power when it comes to occupy the 
point P /; . So that if E should remain fixed during an 
entire revolution of P, a compensation would be effected, 
and the velocity of the planet on reaching its point of 
departure would be identical with that with which it 
started, and hence the major axis, though it would have 
lost and gained, would in the end be restored to its 
primitive value. 

If the orbits were elliptical and their major axes were 
coincident the same reasoning from symmetry would still 
hold good, and demonstrate the restoration of the major 
axis, and as action and reaction are always equal, it is 
manifest that by fixing P and causing E to revolve, the 
changes wrought by E on P would now be wrought by 
P on E, only in the reverse order — that is, wherever P 
was accelerated by E, E will be retarded by P, and vice 
versa. 

Admitting the major axes to be inclined to each other 
destroys the symmetry of the figure, and an exact resto- 
ration is not effected in one revolution ; but as the peri- 
helia of the planetary orbits are all in motion, the lime 

i i 



314 THE SUN AND PLANETS 

will come when a coincidence of the major axes will be 
effected, and if there be a certain amount of outstanding; 
uncompensated velocity, when the coincidence takes place, 
the action will be reversed, and at the end of one grand 
revolution of the major axes from coincidence to coinci- 
dence the restoration will be completed, and the axes will 
return to their primitive value. 

Here we are compelled to leave the problem, and simply 
state the result which a complete solution has effected. 
We are again indebted to Lagrange for the resolution of 
this most important of all the problems involving the 
stability of the solar system, who presents the final result 
as follows : — 

" If the mass of each planet be multiplied by the square 
root of the major axis of its orbit, and this product by the 
square of the tangent of the inclination of the orbit to a 
fixed plane, and all these products be added together, 
their sum will be constantly the same, no matter what 
variations exist in the system. ' ; 

The mass or weight of each planet is invariable, while 
the loss or gain in the values of the major axes is always 
counterpoised by the gain or loss in the inclination of the 
orbits, and thus in the long run, in cycles of vast periods, 
a complete restoration of the major axes is fully accom- 
plished, and the system in this particular returns to its 
normal condition. 

We have thus far considered the effect of two out of 
the three forces into which a disturbing force may be de- 
composed. The normal component remains to be ex- 
amined. This acts in a direction normal to the curve 
described by the planet, or perpendicular to the tangent 
to the orbit at the point occupied by the planet. We 
shall not enter into any extended examination of this sub- 



AS PONDERABLE BODIES. 315 

ject, and will only say that this component of the dis- 
turbing force gives rise to a movement in the perihelion 
points of the planetary orbits, sometimes advancing these 
points, sometimes giving them a retrograde motion, and 
in some instances producing oscillations. 

These effects are necessarily mixed up and combined 
with those produced by the action of the tangential force, 
for, as we have seen, the effect of this force goes to in- 
crease or decrease the value of the major axis ; but no 
increase or decrease of the major axis can take place 
without a corresponding change in the eccentricity, so 
that these changes thus modified, the one by the other, 
finally become exceedingly complex, and can only be 
traced and computed by the application of the highest 
powers of analytic reasoning. 

The complexity is further increased from the fact that 
in the consideration of the entire problem of perturbations 
the varying distances of the disturbing and disturbed 
bodies must be rigorously taken into account, and may 
modify and even reverse the effects due simply to direc- 
tion. With difficulties so extraordinary and diversified, 
with complications and complexities mutually extending 
to each other, involving movements so slow as to re- 
quire ages for their completion, it is a matter of amaze- 
ment that the human mind has achieved complete success 
in the resolution of this grand problem, and can with 
confidence pronounce the changes to fall within narrow 
and inocuous limits, while in the end, after a cycle o( 
incalculable millions of years, the entire system o( planets 
and satellites shall return once more to their primitive 
condition, to start again on their endless cycles of con- 
figuration and change. 

There remains one more source whence arises an ae- 



316 THE SUN AND PLANETS 

cumulation of disturbance, progressive in the same direc- 
tion through definite cycles of greater or lesser duration. 
I mean the effects due to a near commensur ability of 
the periods of revolution of the disturbed and disturbing 
planets. The nearer the approach to commensurability 
the longer will be the duration of the resulting in- 
equality. 

We shall have occasion to resume this subject in our 
examination of the circumstances of disturbance belonging 
to each individual planet, which we shall now proceed 
to examine briefly, commencing at the sun, and proceed- 
ing outwards. 

The sun considered as a gravitating body. — 
We shall now return to the great center of the planetary 
worlds with a full knowledge of the laws of motion and 
gravitation, and provided with the instrumental means 
of securing those delicate measures whereby the solar orb 
may be determined in distance, volume and tveight. 



We have already explained how these quantities may 
be obtained, and we now present the results of exact 
measures and accurate computation. The sun's mean 
distance from the earth may be taken at ninety-five mil- 
lions of miles. By exact measures the mean diameter 
of the sun subtends an angle equal to 32'. 01 ".8, and an 
angle of this value indicates a real diameter in the sun 
of 883,000 miles, as may be seen from the figure above, 



AS PONDERABLE BODIES. 317 

in which it is evident that a line A B subtends at A' B', 
a' much : . smaller angle than when located at A B, nearer 
the vertex. If, then, we have a given angle A 7 E B', 
and a given distance E B', from the vertex, if we erect 
the line B' A! it is evident the length of this line will 
be determined by the value of the angle B'EA' and 
the length of the line EB'; so the sun's distance and 
angular diameter determines his real diameter. This 
diameter of the sun (883,000 miles), in terms of the 
diameter of the earth, amounts to- 111.454, and as the 
volumes of two globes are in the proportion of the cubes 
of their diameters, we shall have the volume of the sun 
to the volume of the earth as (111.454) 3 is to (l) a , or as 
1,384,472 to 1, or it would require no less than one 
million three hundred and eighty-four thousand four 
hundred and seventy-two globes as large as the earth to 
fill the vast interior of a hollow sphere as large as the 
sun. By this we do not mean to assert that the sun 
weighs as much as 1.384,472 earths. This is not the 
fact We have seen already the process by which the 
relative weights of these globes may be reached, and we 
have found that the force exerted on the earth by the 
sun, enfeebled by the distance at which it acts, and 
thus reduced to the 160,000th part of its actual value, 
at a distance equal to that of the moon, still exceeds 
in a more than twofold ratio the force exerted by tho 
earth on the moon ; and when the exact ratio is applied 
we find the weight of the sun to be equal to 354,936 
earths, and this is what we call the mass of the sun. 

If we divide the mass by the volume we obtain the 
specific gravity of the sun, in terms of that of the 
earth, equal to , •^■••^:'.«, — 0.2r>43— that is, the aver- 
age weight of one cubic foot of the sun is only one- fourth 



318 THE SUN AND PLANETS 

as great as the average weight of one cubic foot of the 
earth. 

It is the mass of the sun and not its volume which 
determines the amount of force which this great central 
globe exerts. Its weight is such as vastly to exceed that 
of any one of the planets, and indeed it rises so superior 
to the combined masses of all the planets that the center 
of gravity of the system falls even within the surface of 
the sun. This may be shown by an examination of the 
weights and respective distances of the planets. We will 
explain the reasoning. If the sun and earth were equal 
in weight, then the center of gravity would lie in the 
middle of the line joining their centers ; but the sun is 
equal in weight to 854,936 earths, and hence, dividing 
the distance between the centers (ninety-five millions of 
miles) into 354,936 equal parts, the center of gravity 
of the sun and earth will fall on the first point of division 
nearest the sun's center, that is at a distance of about 267 
miles ; but from the center of the sun to his surface is a 
distance of 440,000 miles, and thus the center of gravity 
of the sun and earth falls far within the limits of the solar 
surface. 

The energy exerted by the sun on any one of his satel- 
lites is in a constant state of fluctuation, growing out of 
the variation in the distance of the planet. The sun's 
force decreases as the square of the planet's distance in- 
creases. If, then, we take the earth's distance as unity, 
and call the force exerted on the earth by the sun one, 
the force exerted on a planet twice as remote from the 
sun as the earth, would be but one-fourth, at three times 
the distance one-ninth, at ten times the distance it would 
be but one hundredth part of that exerted on the earth. 
This law of gravitation should be well understood, as we 



AS PONDERABLE BODIES. 319 

shall have occasion to make frequent applications in our 
future examinations. 

Power of gravitation on the solar surface. — ■ 
If it were possible to transport a body weighing at the 
earth's equator one pound to the equator of the sun, 
as the weight of the body is due to the power of the 
earth's attraction, and as the sun is heavier than the 
earth in the high ratio of 354,936 to 1, we might sup- 
pose that the pound weight on the earth removed to the 
sun would be increased in the same ratio. This would 
be true in case the sun's diameter were precisely equal 
to that of the earth. This, however, is not the case. 
The radius of the sun is 111.454 times that of the earth, 
and this distance will reduce the attractive power of the 
sun in the ratio of (111.545) 2 to (1)\ or as 12,342.27 to 
1. If, therefore, we reduce 354,936 in the above ratio, 
or, in other language, divide it by 12,342.27, we obtain 
for a quotient 28, showing that a body weighing one 
pound at the earth's equator would weigh 28 pounds at 
the sun's surface. This w T ould be slightly reduced from 
the uplifting action of the centrifugal force due to the 
velocity of rotation of the Sun on its axis. This diminu- 
tion may be readily computed. We shall see hereafter 
that the centrifugal force at the earth's equator is equal 
to 2*- ¥ of the force of gravity. Now, if the sun rotated 
in the same time as the earth, and their diameters were 
equal, the centrifugal force on the equators of the two 
orbs would be equal. But the sun's radius is about 111 
times that of the earth, and if the period or rotation were 
the same the centrifugal force at the sun's equator would 
be greater than that at the earth's, in the ratio of (Hl) a 
to 1, or more exactly in the ratio oi' 12,842.27 to 1. But 
the sun rotates on its axis much slower than the earth, re- 



320 THE SUN AND PLANETS 

quiring more than 25 days for one revolution. This will 
reduce the above in the ratio of 1 to (25) 2 , or 1 to 625 ; 
so that we shall have the earth's equatorial centrifugal 
force ^Ag x 12,342.27-^625= l - a tH?iU = 0.07 nearly 
for the sun's equatorial centrifugal force. Hence the 
weight before obtained, 28 pounds, must be reduced seven 
hundredths of its whole value, and we thus obtain 28 — 
0.196=27.804 pounds as the true weight of one pound 
transported from the earth's equator to that of the 
sun. 

These principles enable us to compute readily the 
gravitating force exerted by the sun at any given dis- 
tance ; and, as we shall see hereafter, this mighty cen- 
tral orb is pre-eminently the controlling body in the 
scheme of revolving worlds, which move about him as 
their center, in obedience to the laws of motion and 
gravitation. 

We close what we have to say of the sun by stating 
that a heavy body weighing, as it does, 27.8 times as much 
at the solar as at the terrestrial equator, if free to fall, 
will pass over in one second a space equal to 27.8 x 16.1= 
247.58 feet. 

Perturbations of mercury. — In our discussion of 
the planets already given we were only prepared to pre- 
sent the discoveries of formal astronomy. These in- 
volved the elements of the elliptic orbits and the ob- 
served circumstances of the planetary movements. We 
are now prepared to understand how the system of solar 
satellites constitutes a grand assemblage of worlds in 
motion and yet in equilibrio, so that, although there be 
fluctuations to and fro, which are really perpetual, in the 
end the system is stable and in exact dynamical counter- 
poise. The great law of universal gravitation being 



AS PONDERABLE BODIES. 321 

known, as also the laws of motion, it becomes possible 
to determine the exact conditions of this mighty system- 
atic equilibrium, and in a strict sense to weigh each of 
the worlds belonging to the system. Indeed, this weight 
or mass of the planets must be first ascertained before it 
becomes possible to compute the influence exerted by one 
body on another, even when their actual distances are 
known. The distances being the same, two bodies at- 
tract a third by a force which is in direct proportion to 
their masses. Hence, if our moon could be conveyed suc- 
cessively to each of the planets and be located at the same 
distance from each it now is from the earth, the periods 
of revolution of our satellite round any one of these worlds 
would show us whether that world weighed more or less 
than ours. Thus in case the period of revolution of the 
moon around a planet should be one-half its present 
period, then that planet, holding, as it does, the moon 
with double the velocity at the earth, it must be double 
the weight of the earth, and so for any other period. 

It is in this way that we are enabled very exactly to 
weigh the planets which are surrounded by satellites, as 
we have already seen ; but those planets which have no 
satellite, such as Mercury, Venus and Mars, can only be 
weighed by the effect they produce on other bodies of 
the S} r stcm, and especially on those vaporous masses the 
comets, which occasionally come sufficiently near these 
bodies to be subjected to very powerful perturbations. 

The mass of Mercury is, of course, subject to some 
uncertainty, but as now determined, in case the sun were 
divided into one thousand millions of equal parts, it 
would require 2,055 of these parts to be placed in one 
scale of a balance to counterpoise Mercury in the oppo- 
site scale. 

14* 



322 THE SUN AND PLANETS 

Knowing the mass of a planet and its volume, we can 
easily deduce its specific gravity or density. For ex- 
ample, the volume of Mercury is equal to 0.595, the 
earth being unity ; but the mass of the earth in the same 
parts of the sun just employed, as we shall see, is 28,173. 
Hence, if these planets were equally dense, their volumes 
would be to each other as 28,173 to 2.055, or nearly as 
13.7 to 1, or as 1 to 0.072 ; but Mercury's volume is but 
0.595. the earth being taken as unity, and hence Mer- 
cury must be denser than the earth in the ratio of 0.072 
to 0.595, or as 1.2 to 1 nearly. 

Thus are we made acquainted with the very structure 
or material of the planets by the process of weighing 
them, revealed by the laws of motion and gravitation, and 
that these results cannot be much in error is manifest 
from the fact that the transit of Mercury across the 
sun's disk, which occurred on the 8th May, 1845, and 
observed at the Cincinnati Observatory, the computed 
and observed contact of the planet with the sun's- limb 
differed by only sixteen seconds of time ! 

This prediction also verifies the values of the secular 
inequalities, or slow changes in the element of Mercury's 
orbit, due to the planetary perturbations, which were 
fixed for the beginning of the present century as fol- 
lows : — The perihelion makes an absolute advance each 
year of 5". 8 ; the node recedes annually 7". 8. The 
eccentricity, in terms of the semi-major axis, was 
0.210.551.494, and its decrease in one hundred years 
amounts to 0.000.003.866, in terms of the same unit. 
Let us admit these changes to be progressive at the 
same rate, and then convert them iuto intelligible terms, 
and examine the results. The perihelion point advanc- 
ing at the rate of 5 ".8 a year, will require to pass over 



AS PONDERABLE BODIES. 323 

360°, or 1,296,000 seconds, ^-^-- = 223,449 years. 
Such is the vast period required for one revolution of 
the perihelion point. In like manner we may see that 
the node requires a period exceeding one hundred thou- 
sand years for its revolution. 

The eccentricity is slowly wearing away, the orbit 
becoming more nearly circular, and if this change pro- 
gresses uniformly, it will require no less than five mil- 
lion four hundred and forty-six thousand two hundred 
years to reduce the figure of Mercury's orbit to that of 
an exact circle ! 

The present eccentricity of the orbit of Mercury is 
such that the aphelion distance exceeds the perihelion 
distance by more than fifteen millions of miles. The 
energy exerted by the sun on the planet at perihelion, 
as compared with that exerted at aphelion, may be read- 
ily computed thus : Mercury's greatest distance from the 
sun amounts to about forty-four millions of miles. This 
is about ten times the solar radius, and at this distance 
the sun's power will be reduced to the one hundredth 
part of what it is at the sun's surface, but the planet 
when nearest the sun is distant about twenty-nine mil- 
lions of miles, that is, less than seven times the solar 
radius, and hence the power of gravitation is reduced to 
the one forty-ninth part of what it is at the sun's sur- 
face, or, what comes to the same thing. Mercury at ap- 
helion is attracted with a force only one-half as great as 
that by which it is affected when nearest the sun. 

If a person were transported to the equator of Mer- 
cury his weight would be greatly reduced from that found 
on the earth. The mass of Mercury, in terms o( that o[ 
the earth as unity, is but 0.729. and if Mercury's diam- 
eter were equal to that of the earth, then one pound on 



324 THE SUN AND PLANETS 

the earth would weigh 0.729 lbs. when removed to 
Mercury ; but as the radius of Mercury is only 1,544 
miles, or twenty-six hundredths of the earth's radius, 
this will increase the weight in the ratio of (2.6) 2 to (l) 2 , 
or as 6.76 to 1. Hence, by multiplying 0.729 by 6.76, 
we have 0.493 lbs. as the weight of a terrestrial pound 
removed to Mercury, that is, the power of gravitation 
on the surface of this planet is about one-half of what it is 
on the earth. 

All the planets exterior to the orbit of Mercury exert 
an amount of power on this nearest planet to the sun 
which varies directly as the mass, and inversely as the 
square of the distance of the disturbing body. Let us 
suppose the earth and Venus to be in conjunction with 
Mercury, and that these planets are at their mean dis- 
tances from the sun, and let us compute in this configu- 
ration the relative power of the sun, of Venus, and of the 
Earth, over Mercury. 



L 

JM. 



In the figure let S represent the sun, M Mercury, V 
Venus, and E the Earth. Taking the distance S E to be 1. 
S M will be 0.387, and S V will be 0.723. Hence, M V 
will be equal to S V-S M=0.723-0.387=0.336, and 
V E will be equal to S E-S V -=1.000-0.723-0.277. 
As the mass of Venus is but the 390,000th part of the 
sun's mass, her effect on Mercury at equal distances 
would be but one part in three hundred and ninety 
thousand of the sun's power. The fact that Venus is 



AS PONDERABLE BODIES. 325 

nearer Mercury than the sun, in the ratio of Y M to S M, 
or of 0.336 to 0.387, will increase her relative power in 
the ratio of the squares of these quantities inversely, 
that is, as (0.336)' J to (0.387) 2 , or as 0.113 to 0147, or 
as 1 to 1.3 — that is, we must multiply ^^^ by 1.3 
to obtain the effect of Venus on Mercury, as compared 
with that of the sun ; in other language, if the sun's 
power over Mercury be divided into 390,000 equal parts, 
the power of Venus over the same planet will amount to 
just one and one-third of these parts. 

Let us now compute the attraction of the earth as 
compared with that of the sun. As the earth weighs 1, 
while the sun weighs 354,936, at equal distances the 
powers of the earth and sun would be as 1 to 354,936 ; 
but the distance S M is 0,387, while the distance M E 
is 1.000 — 0.387=0.613. As the sun is the nearer, his 
power will be increased in the ratio of the square of dis- 
tance inversely, or as (0.613) 2 to (0.387) 2 , or as 0.376 
to 0.147, or as 2.56 to 1 — that is, the earth's power, 
which on account of its mass is but one part in 354,936 
of that of the sun at equal distances, must further be re- 
duced on account of its distance to a fraction of this quan- 
tity, represented by j} 1Ti that is, in case we divide the 
sun's power of attraction upon Mercury into 787,340 
parts, the attractive power of the earth will be repre- 
sented by one of these parts. 

We have seen above that tho power of Venus over 
Mercury is equal to 3 7 £:!tir> tnc power of the sun being 
1. The power of the earth is TT y. T1 ; ,, or not quite one- 
half of the former quantity. Hence the disturbing in- 
fluence of Venus is evidently the predominating one In 
tlio case of Mercury. 

It may be well to extend our investigation a little 



326 THE SUN AND PLANETS 

further and examine the influence of the massive planet 
Jupiter on Mercury, to see whether Venus still pre- 
dominates in its power over that of the heaviest planet 
of the system. The distance of Jupiter from the sun is 
5.2, that of the earth being 1. The distance of the earth 
from Mercury is 0.613. The distance of Jupiter from 
Mercury is 5.200-0.387=4.813. In case the earth 
and Jupiter were equal in mass, then the power of Jupi- 
ter over Mercury would be to the power of the earth as 
(0.613) 2 to (4.813) 2 , or as 0.376 to 23.164, or as 1 to 
61.6 — that is, Jupiter's effect is reduced to the fraction 
F }g of what it would be at a distance from Mercury equal 
to that of the earth ; but this is supposing the earth and 
Jupiter to be equal in mass, whereas Jupiter really re- 
quires 338 earths to counterpoise his weight. We must, 
therefore, increase the fraction F | j 338 times, and we 
have -§f\=5.5 about. Hence, Jupiter exerts a power 
over Mercury when in conjunction 5S times as great as 
that exerted by the earth, or two and a half times greater 
than the attraction of Venus. 

These computations have been made to show how min- 
ute a portion of the sun's power is that exerted by any 
planet to disturb the motions of another planet, and also 
to show that we cannot neglect any disturbing body be- 
cause of the great distance at which it may be placed. 

It will be readily seen that when Mercury is in oppo- 
sition with respect to Venus, her power is greatly re- 
duced on account of the increased distance by which the 
planets will be then separated. Indeed, the attractive 
force computed at conjunction will be reduced to about 
one-tenth at opposition. 

This is not true, however, of the attractive power of 
Jupiter. The distance 4.813 in conjunction will only be 



AS PONDERABLE BODIES. 327 

increased by the diameter of Mercury's orbit, or by 
2(0.387) — 0.774 when in opposition, and the distances 
will stand 4.813 and 6.587. Jupiter's power at the in- 
creased distance will be reduced only in the ratio of the 
square of 4.813 to that of 6.587, or about as 1 to 2. 

As an exercise the student should compute the energy 
exerted by the other planets over Mercury, and thus ob- 
tain a familiarity with the application of the law of gravi- 
tation to the problems of nature. 

While we are writing the intelligence has reached this 
country that a new planet has actually been discovered, 
revolving in an orbit between Mercury and the sun. 
M. Le Verrier some time since announced that there 
were perturbations in the elements of the orbit of Mer- 
cury not explained by any of the known causes, and 
hence he drew the conclusion that possibly a ring of very 
small planets were revolving within the limits of Mer- 
cury's orbit. One of these minute planets is said to have 
been actually seen more than once by an amateur as- 
tronomer, whose name is M. Lescarbault. This planet is 
said to complete its revolution in about three weeks, and 
hence its distance from the sun must be about fourteen 
or fifteen millions of miles. 

Venus considered as a ponderable body. — The 
angle subtended by this planet at its mean distance from 
the earth amounts to 17 .55, showing an actual diameter 
nearly equal to that of the earth. The weight or mass 
of Venus is not so well determined as that of the planets 
attended by satellites, yet we have reason to believe that 
the approximate value does not differ by any very con- 
siderable amount from the true one. As now deter- 
mined by the best authorities, Venus weighs 0.^00, ihe 
weight of the earth being assumed as 1 .000. If an in- 



328 THE SUN AND PLANETS 

habitant of the earth were transported to Venus, his 
weight would be reduced in the ratio of 1 to 0.94, and a 
heavy body, free to fall, would pass over 15.1 feet in the 
first second of time. Here we might repeat the reason- 
ing already employed in the case of the sun to reach 
these results, but as we shall have occasion hereafter 
to apply the reasoning to the cases of the larger plan- 
ets, we shall merely refer to the demonstration already 
made. 

All the elements of the orbit of Yenus are in a state of 
constant fluctuation. The exact condition of these elements 
will be given hereafter, as well as the measured amount of 
the changes. We find in Venus the first example of a re- 
markable perturbation arising from a cause already ad- 
verted to, viz. : an approximate commensurability between 
the periods of revolution of Venus and the earth. The 
planet performs her revolution around the sun in 224.700 
days, while the earth occupies 365.25 days in accom- 
plishing her revolution. If we multiply 224.7 by 13 we 
obtain 2,921.10 ; multiply 365.256 by 8, and we have 
2,922.048. Thus we perceive that in case Venus and 
the earth are in conjunction on any given day, at the end 
of 2,921 days they will be nearly in conjunction again at 
the same points of their orbits. Whatever perturbation 
the one planet produces on the other will be again re- 
peated on the return of the same identical configuration. 
But we have already seen that the synodical revolution 
of Venus is accomplished in 583.9 days. This quantity, 
multiplied by 5, produces 2,919.6 — that is, during the 
time involved in the long cycle of 2,921 days there have 
occurred five conjunctions of the earth and Venus dis- 
tributed equally around the orbits of the planets. If we 
examine the figure below, and suppose S, V and E to 



AS PONDERABLE BODIES. 



329 



represent the places of the sun, of Venus and the earth, 
at the. commencement of a great cycle of 2,921 days, at 
the end of one synodic revolution of Venus V 7 and E' 
will be the places of the two planets. At the end of the 

E 




second synodic revolution the planets will be in V and 
and E", and thus they will pass round the orbits, mak- 
ing their conjunctions at intervals of 583.9 days, and 
separated by arcs equal to one-fifth part of 360°. Let 
us now carefully examine the reciprocal influence of V 
and E. Starting from the places V and E in the figure, 
Venus will take the lead, and will tend to drag forward 
the earth, while the earth will pull back the planet, and 
as the planets swoop around the sun, Venus overtakes the 
earth at W" E"", and as the earth is now in advance, 
it will accelerate Venus, and will in turn be retarded. 
Thus a partial compensation is effected, and the motions 
of the planets return nearly to what they were at the 



330 THE SUN AND PLANETS 

start. This same process is repeated at every conjunc- 
tion ; and in case the planets fall exactly on the right 
line SVE. at the end of five of these conjunctions a 
complete restoration would be effected. But this is not 
exactly true. The periods are not precisely equal, and 
the fifth conjunction does not fall on S V E, but on a 
dotted line a little behind the position SVE. There 
will, therefore, remain a very small amount of outstand- 
ing perturbation at the close of one great cycle, which 
will go on accumulating so long as the dotted line falls in 
the same half of the earth's orbit. But the difference 
between 2,921.160 days and 2,922.048 is 0.852, and by 
this fraction of one day is the earth later than Venus in 
reaching the point of departure. Hence, the conjunction 
of the planets must have taken place on a line behind 
that of the former conjunction, whose position may be 
readily computed. The daily motion of Venus is 1°. 6 12, 
while that of the earth is 0°.985, and thus Venus gains 
daily on the earth by an amount equal to 1°.612 — 
Q .985=0°.627. Let S V E be the line of the first 

w L 



/Y'<- 



E 



if 

E 



conjunction. At the end of thirteen revolutions of Venus 
she returns to the point V, while the earth is in the 
point E', requiring yet 0.852 days to reach E. Venus 
must, therefore, have passed the earth on some line as 
S V" E' 7 , such that Venus will have gained 0.852 days 
on the earth when she arrives at V. But the daily mo- 
tion of Venus is 1°.612, and in the fraction of one day 
0.852, she will move l°.612x0.852=l°.373. Hence, 



AS PONDERABLE BODIES. 331 

the new line of conjunction S V /; E" must fall behind 
the old line by this amount in each great cycle of thir- 
teen revolutions of Venus and eight revolutions of the 
earth. 

At the end of a great cycle, formed by dividing 3G0° 
by 1°.373, and multiplying the quotient by 8, the line 
of conjunction will return to its former position ; and in 
case the orbits remain circular, all the perturbations of 
both the planets resulting from this cause, as affecting 
the orbital velocities and consequently the lengths of the 
major axes, will have been completely obliterated. The 
orbits are. however, not exact circles, neither are the 
elements invariable, and hence the restoration will not 
be perfect even at the end of this great cycle; but as the 
changes are all periodical, and as the lines of apsides re- 
volve entirely around, periodicity again marks these 
minute perturbations, and at the end of a grand cyclo, 
composed of many subordinate ones, these complexities 
and modifications will all be entirely swept away, and 
the system return to its primitive condition. The singu- 
lar equation (as it is called) above described in the mean 
motions of Venus and the earth was first detected by 
the present Astronomer Royal. The period is about 240 
years, and in the whole of this time the accumulated 
effect on the longitude of Venus cannot exceed 2". 95, 
while its effect on that of the earth only reaches 2". 06. 
This result of computation yet remains to be verified by 
actual observation. 

For other particulars of the characteristics of this 
planet and of the elements of its orbit we refer the 
reader to the Appendix:. 

The earth and moon as ponderable bodies. — We 
have already determined the weight of the earth in tonus 



332 THE SUN AND PLANETS 

of that of the sun, and we have seen that it would require 
354,936 earths like ours to balance the ponderous orb 
which occupies the focal point of the solar system. It 
remains now to determine the absolute weight of the 
earth in pounds avoirdupois. We shall assume water as 
the standard, and admit that one cubic foot of water 
weighs 62.3211 lbs. From the known magnitude of the 
sphere of the earth, assuming, say, the mean diameter to 
be 7,941.12 miles, we can obtain the solid contents in 
cubic miles, amounting to no less than 259,373 millions. 
The number of cubic feet in a cubic mile is readily com- 
puted, being equal to 5,280x5,280x5,280. Thus if 
we knew the weight of one cubic foot of the earth, in 
terms of the weight of one cubic foot of water, the total 
weight of the entire globe could be readily obtained in 
pounds. 

This weighing of the earth, absolutely, is a problem of 
great difficulty, yet it has been executed, and the final 
results, though not precisely accurate, are, no doubt, 
close approximations. We can only give a general out- 
line of the principle involved in the method employed. 
Suppose an inflexible rod with a small leaden ball at 
each extremity suspended in the middle by a delicate 
wire. When absolutely at rest the wire will hang ver- 
tically without twisting or torsion. Any force applied 
to either leaden ball to move it horizontally will tend to 
twist the suspending wire, and this torsion will resist the 
action of the force, and this resistance will finally be 
brought into equilibrium with the force, and will thus in 
some sense become its measure. Thus in case a delicate 
weight is attached to one of the leaden balls and suspended 
over a pulley, it will descend until the torsion of the 
wire shall be such as to exactly balance the small weight, 



AS PONDERABLE BODIES. 333 

and then the torsion and weight will stand in equilibrio, 
and the value of the weight (friction out of considera- 
tion) measures the force of resistance to torsion. Sup- 
pose a divided scale placed beneath the leaden ball, and 
a needle used as a pointer, then as the ball moves over 
this scale, a microscope properly adjusted may read the 
amount of motion with the greatest delicacy. 

This machinery being arranged, suppose we bring a 
leaden ball one foot in diameter to within, say six inches 
of the small ball. Its power of attraction will move this 
ball over a space easily read off from the divided scale, 
and this will measure the attractive force of the large 
leaden ball. 

Having thus learned the power exerted by a leaden 
ball one foot in diameter, on a material point located one 
foot from its center, it is easy, from the principles already 
laid down, to compute what would be the attractive 
poAver of a globe of lead as large as the earth ; and in 
case this power of attraction thus computed should be 
precisely equal to that exerted by the earth, then the 
earth must weigh exactly as much as the leaden globe of 
equal size. This, however, is found from many experi- 
ments, tried with the most refined apparatus, not to be 
the case. The leaden globe is much heavier than the 
earthen one, and, indeed, we find that one cubic foot of 
earth of the mean density of the whole globe is as heavy 
as about five and a half cubic feet of water. Hence, 
every cubic foot of the earth weighs on the average 
G2.3211 x 5.5 = 342.76 lbs. ; and as there are in the en- 
tire globe 250,373 millions of cubic feet, the whole globe 
must weigh 342.70x259,373 millions of pounds avoir- 
dupois. 

With this knowledge oi' the absolute weight of our 



334 THE SUN AND PLANETS 

earth it is easy to obtain the weight of the sun and plan- 
ets in pounds, were it necessary. Multiply the number 
of pounds in the weight of the earth by 354,936, and we 
obtain the actual weight of the sun. 

The figure of the earth.— We have already seen 
that the earth is not a sphere, but a spheroid, protuber- 
ant at the ?quator and flattened at the poles. The exact 
methods of astronomy employed in the measurement of 
arcs of the earth's meridians, together with the vibra- 
tions of the pendulum in different latitudes, have fixed 
with great accuracy the relative values of the polar and 
equatorial diameters of the earth. The mean of a large 
number of measures results in giving the — 

Equatorial diameter, 41. 84?, 192 feet. 

Polar diameter, 41,707,324 " 

This gives a compression of ... . 139,768 " 

Some very remarkable results flow from this peculiar 
figure of the earth. Among these we shall consider first 
the equilibrium of the ocean. If it be true, as just 
asserted, that the equatorial diameter of our globe ex- 
ceeds the polar diameter by 139,768 feet, then in case 
the earth were reduced to the figure of an exact sphere, 
by turning off the redundant matter, we should be com- 
pelled to turn down at the equator, to a depth of no less 
than 69,884 feet (one-half of the above quantity), and 
hence the equatorial region may be considered as a vast 
mountain range, belting the whole earth, and rising 
above the general level nearly seventy thousand feet. 
On the sides and over the summit of this mountain range 
the ocean sweeps its currents and its tides, and yet the 
most delicate and beautiful equilibrium is maintained. 

This is due to the fact that the velocity of rotation of 



'as ponderable bodies. 335 

the earth on its axis is absolutely uniform and invariable, 
and hence the centrifugal force, whose power precisely 
counterbalances the gravity on the mountain side on which 
the ocean rests, is ever the same. This great principle is 
beautifully exemplified by taking a glass vase, filling it 
with a colored liquid, and suspending it by a cord. So 
long as the vase is at rest the fluid on its upper surface is 
precisely level and plain. Now, give to the vase a mo- 
tion of rotation about a vertical axis (as by the untwist- 
ing of the suspending cord), and at once the fluid com- 
mences to rise upon the sides of the vase, and a disk-shaped 
cavity is formed. This rising continues so long as the 
velocity of rotation increases. Should the velocity be- 
come uniform, then the figure of the fluid in the vase 
assumes a form of exact equilibrium, and the delicate 
circle that marks the height to which the fluid rises in 
the vase remains constant, and will so continue, so lon^ 
as the velocity of rotation is unchanged. The stability 
of the figure of the ocean depends on the same principle, 
and were it possible to arrest the rotation of the earth, 
instantly the equatorial ocean would rush towards the 
poles and would there rise until the general level should 
become such as is due to a spherical figure, which the 
ocean would assume. 

Nutation and precession. — We have in these re- 
markable phenomena another effect of the figure of the 
earth. We have already mentioned the fact that the 
vernal equinox (the point in which the sun's center 
crosses the equinoctial in the spring season), does not re- 
main fixed in the heavens. This discovery was made by 
the early astronomers, the fact noted, and an approximate 
period of revolution, amounting to some twenty-five or 
twenty-six thousand years. Modem science has not only 



836 THE SUN AND PLANETS 

determined the exact period to be 25.868 years, but has 
traced the phenomenon to its origin, and has revealed the 
cause to lie in the fact that the protuberant mass of mat- 
ter surrounding the equator of the earth is a sufficient 
purchase to enable the sun and moon to tilt the entire 
earth, and consequently the plane of the earth's equa- 
tor. Suppose the earth revolved on an axis perpen- 
dicular of the ecliptic, or that the equator of the earth 
and the ecliptic coincided. Then, so far as the sun is 
concerned, there could arise no power to effect a change 
in the plane of the equator ; but as the moon revolves in 
an orbit inclined to the plane of the ecliptic, the moon 
will be sometimes above and sometimes below the plane 
of the earth's equator, now supposed to be coincident 
with the ecliptic. Whenever the moon is above the equa- 
torial ring of the earth, she will tend to lift the nearest 
portion of that ring above the ecliptic, and to sink the 
opposite part below the same plane, and as the moon re- 
volves around the earth, she will cause the equatorial 
ring to tilt towards her position, and thus the line of 
nodes of the ring will revolve as do the lines of nodes of 
the planetary orbits ; and this is precisely what we find 
to be true of the line of equinoxes, or the line cut by the 
plane of this equatorial ring from the plane of the eclip- 
tic, producing, as we have seen, a retrocession of the 
equinoctial point, and a precession of the time of the 
equinox. 

The nutation of the earth's axis is a phenomenon 
springing out of the same causes producing precession. 
If we consider the axis of the earth as an inflexible bar, 
passing through the earth's center and perpendicular to 
the equator, extending indefinitely in opposite directions, 
to the celestial sphere, it is clear that any tilting of the 



AS PONDERABLE BODIES. 337 

earth's equatorial ring will equally tilt the axis of the 
earth, This is actually seen in the slow revolution of 
the pole of the earth's equator around the pole of the 
ecliptic in a period precisely equal to that employed in 
the revolution of the equinoxes. Nutation is but a su- 
bordinate fluctuation whereby the pole of the equator, 
instead of describing an exact circle around the pole of 
the ecliptic, makes certain short excursions a little on the 
inside and on the outside of this circle, in a period which 
agrees exactly with that occupied by the revolution of the 
nodes of the moon's orbit. This at once suggests the 
moon to be the principal cause of this nodding of the 
earth's axis, and, indeed, modern analysis has pointed out 
the origin of the movement, and has accurately computed 
its value. 

In all we have said we have supposed the equator and 
ecliptic to coincide. This, however, is not the case of 
nature. These planes are inclined to each other, and 
hence we find the sun producing results (analogous to 
those already traced to the moon) on the mass of pro- 
tuberant matter surrounding the earth's equator. The 
exact values of these constants of precession and nuta- 
tion will be found in the Appendix. The greatest pains 
have been bestowed on their determination, as they are 
of the first importance in fixing the absolute places of all 
the heavenly bodies. 

Figure of the earth's orbit. — The ellipticity of 
the earth's orbit is slowly wearing away, under the com- 
bined influence of all the planets. The eccentricity at 
the commencement of the present century amounted to 
0.016783568, the semi-major axis being considered as 
unity. The amount by which this quantity is decreased 
in a hundred years is 0.0000 I L63, Let us reduce those 

16 



66$ THE SUN AND PLANETS 

figures to intelligible quantities. The eccentricity is the 
distance from the center of the ellipse to the focus, and in 
miles is equal to 0.016783568 x 95,000,000=1,594,100. 
This quantity decreases in one hundred years by 
0.00004163x95,000,000=3,954.85 miles. If, now, 
we divide 1,594,100 by 3,954.85, the quotient 405+ will 
be the number of centuries which must elapse before the 
earth's orbit will become an exact circle at the present 
rate of change. It is ascertained by a rigorous analytical 
investigation of this great problem that so soon as the 
circular figure is reached by the earth's orbit the same 
causes reverse their effects, and the circular figure is lost, 
and the eccentricity of the elliptic figure slowly increases 
until finally, at the end of a vast period, the original form 
of the orbit is regained, to be again lost, and thus an ex- 
pansion and contraction marks the history of the earth's 
orbit, vibrating through periods of time swelling into mil- 
lions of years. 

Acceleration of the moon's mean motion. — This 
change in the figure of the earth's orbit produces a 
minute change in the mean motion of the moon, which 
was, after long years of the most laborious research, 
finally traced to its true origin by La Place. The fact 
that the moon was moving faster in modern than in 
ancient times became evident from a comparison of the 
modern and ancient eclipses. These eclipses can only 
occur when the sun, earth and moon occupy the same 
right line nearly, and hence their record gives a very 
precise knowledge of the relative position of these three 
bodies. It thus became manifest that the average speed 
with which the moon was moving in her orbit was slowly 
increasing from century to century. This follows neces- 
sarily from the fact that the loss of eccentricity by the 



AS PONDERABLE BODIES. 389 

orbit removes the earth by a small amount (on the aver- 
age) further from the sun. This carries both the earth 
and her satellite by so much away from the disturbing 
influence of the sun, leaving to the earth a more exclusive 
control of the moon. As the sun is outside the moon's 
orbit with reference to the earth, his attraction will in- 
crease the magnitude of the moon's orbit, and, of course, 
her periodic time. Any diminution of the sun's disturb- 
ing power will therefore by so much permit the moon to 
approach the earth, and to increase her velocity of revo- 
lution ; and this is precisely what observation has re- 
vealed with reference to our satellite during the entire 
period that history has recorded the progress of as- 
tronomy. 

This gradual acceleration must continue up to the time 
when the earth's orbit shall become exactly circular in 
form. This limit once attained, as this orbit slowly re- 
sumes its elliptic form, the acceleration of the moon's 
mean motion is converted into retardation, and thus at 
the end of a mighty period this change will be entirely 
destroyed, and the moon and earth return to their primi- 
tive condition. This acceleration of the mean motion of 
the moon is so slow that from the earliest record of 
eclipses by the Babylonians down to the present time, 
some 2,500 years, the moon has got in advance of her 
mean place by about three times her own diameter. 

The facts above related indicate with how much dili- 
gence the moon's motions have been studied. Though 
she is our nearest neighbor, and consequently more di- 
rectly under the eye of the astronomer than any other 
heavenly body, her motions have been more complex and 
difficult of perfect exposition than any object in the 
heavens. The recent investigations of the European and 



340 THE SUN AND PLANETS 

American astronomers and mathematicians seem to have 
finally conquered -this refractory satellite, so that now it 
becomes possible to unravel her involved and intricate 
march among the stars with such precision that we 
can fix her place with certainty for even thousands of 
years. 

Mars as a ponderable bodt. — This planet revolves 
in an orbit of such eccentricity as to present very marked 
differences in the power of attraction of the sun on the 
planet when at its greatest and least distances. Its mean 
distance is 142 millions of miles, giving its semi-major 
axis a length equal to 71 millions of miles. The eccen- 
tricity of the orbit (the distance between the center and 
focus of the ellipse) amounts to nearly one-tenth of this 
quantity, or to about 6.4 millions of miles. Hence, the 
perihelion distance is 64.6 millions of miles, while the 
aphelion distance is 77.4 millions of miles. The attrac- 
tive power exerted by the sun in perihelion will be 
greater than that exerted in aphelion in the ratio of 
(77.4) 2 to (64.6) 2 , or as 5,991 to 4,172, or nearly as 3 
to 2. To resist this increased power of attraction in 
perihelio the planet must there move with a far higher 
velocity than when in its aphelion. All these deductions 
from theory are verified by observation, 

It was from an examination of the movements of Mars 
that Kepler deduced his celebrated laws. These laws we 
have had occasion to use constantly in our computations, 
but in consequence of the mutual actions of the planets, 
not one of these laws is rigorously true. The orbits of 
the planets are not exact ellipses, nor do they so revolve 
that the lines joining them with the sun sweep over pre- 
cise equal spaces in equal times, nor are the squares of 
the periods of revolution precisely proportional to the 



AS PONDERABLE BODIES. 341 

cubes of the mean distances ; but the failure in these 
laws is due entirely to mere perturbation, and in case a 
single planet existed revolving around the sun, they 
would all be scrupulously fulfilled. 

The planet Mars was, however, well situated for the 
examination conducted by Kepler. This becomes mani- 
fest if we call to mind the great distance separating Mars 
and Jupiter, and the comparatively small disturbance 
which the earth can produce. To present this problem 
still clearer let us suppose the earth, Mars and Jupiter to 
be in conjunction, and situated as in the figure. Then 



\E M 



the distance from S to E is 95 millions of miles, from S 
to M 142 millions, from S to J 890 millions of miles. 
Hence, the distance E M is 142 — 95=47 millions of 
miles, while the distance M J is 890 — 142 = 648 millions 
of miles. We will first compute the power of attraction 
of Jupiter on Mars, as compared with the power of the 
sun. If the masses were equal the energy of Jupiter 
would, on account of the greater distance, be reduced be- 
low that of the sun in the ratio of (142) J to (648)*, or 
nearly as 1 to 21. But the masses are not equal, for the 
sun weighs as much as 3,502 such globes as Jupiter, 
and hence, by combining these causes of reduction. Ave 
find the force exerted by Jupiter to be less than that 
exerted by the sun in the ratio of 1 to 3,502 x21, or as 
1 to 115,542. 

Let us now seo what force the earth exerts on Mars, 
when compared with the sun's force. As the earth is 



342 THE SUN AND PLANETS 

nearer to Mars than the sun, in case the sun and earth 
were of equal weights their energy at Mars would be in 
the ratio of (142/ to (47) 2 , or as 20,164 to 2,209, or 
nearly in the ratio of 9 to 1. But the sun weighs as 
much as 354,936 earths, and if we divide 354,936 by 9, 
we obtain 39,437 as a quotient, and hence the power of 
the sun on Mars is to the power of the earth as 39,437 
to 1. 

It is thus seen that the earth is more powerful than 
Jupiter to disturb Mars in the ratio of 115,542 to 39,437, 
or in the ratio of about 3 to 1. To exhibit more clearly 
the minute character of the effects of the earth and of 
Jupiter on this planet, let us compute the space through 
which a body would fall in one second, if as far removed 
from the sun as Mars. We have already seen that 
gravity at the solar surface is 28.7 greater than at the 
surface of the earth. At the earth gravity impresses 
such a velocity on a falling body that it passes over a 
space of 16.1 feet in the first second of time ; therefore, 
a body at the sun's surface would fall through a space 
represented by 28.7 x 16.1=461 feet in the first second 
of its fall. If we remove the falling body to double the 
distance from the sun's center, the force of the sun's 
gravity is reduced to one quarter, and hence the space 
passed over by the falling body at two units from the 
center of the sun will be ^-=115.25 feet. But Mars' 
distance from the sun is 142 millions of miles, while the 
solar radius is 441,500 miles ; in other words, a falling 
body, removed to the distance of Mars from the sun, is 
about 32 times more remote from the sun's center than 
when on the sun's surface, and the energy of the sun's 
gravity would be reduced at this distance in the ratio of 
(l) 3 to (32) 2 , or as 1 to 1,024; so that a body would fall 



AS PONDERABLE BODIES. 343 

in one second, if as far removed from the center of the 
sun as is the planet Mars, through a space represented 
by r *^ T ;== 0.450194 feet. To what extent will this 
quantity be affected by the attraction of the earth ? The 
answer is given in the result already reached that the 
power of the earth is only the thirty-nine thousand four 
hundred and thirty-seventh part of that of the sun, and 
hence the falling body will only pass over the additional 
space represented by the minute fraction Az -^^H-= 
0.000011, or about the one hundred thousandth part of 
one foot. These quantities look to be minute and quite 
unworthy of notice, and yet from these small disturbing 
effects, accumulating through ages, arise all the amazing 
changes which are progressing among the elements of the 
planetary orbits. 

We will not extend these details, but refer for further 
particulars to the Appendix. 

The asteroids as ponderable bodies. — As yet we 
have no certain knowledge of the magnitude or masses 
of these minute worlds. We are assured that they are 
subjected to the laws of motion and gravitation, and that 
the elements of their orbits are undergoing the same 
modifications to which the elements of the orbits of all 
the planets are subjected. These planets are disturbed 
principally by the action of Jupiter, as we may readily 
determine by an examination of the masses and distances 
of the two nearest planets, inside and outside the orbits 
of the asteroids. 

The mean distance of the group from the sun is about 
2.5 times the earth's distance. The distance of Mars, in 
terms of the same unit, is 1.5, and the distance of Jupi- 
ter from the sun is 5.2. Hence, from the mean distance 
of the asteroids to Jupiter is 5.2 — 2.5 = 2.7. and from the 



344 THE SUN AND PLANETS 

same to Mars is 2.5—1.5 = 1.0. Hence, if Mars and 
Jupiter were equal in weight, the power of Mars over the 
central asteroid would exceed the power of Jupiter in the 
ratio of (2.7) 2 to (1.0) 2 , or in the ratio of 7.3 to 1. But 
Jupiter is 256 times heavier than Mars, and hence his 
power will be increased in like proportion, and the at- 
traction of Mars will be to that of Jupiter as 7.3 to 256, 
or as 1 to 35 nearly. Hence we perceive that Jupiter is 
the principal disturber in the movements of the asteroids. 
Eor further particulars the reader will consult the 
Appendix. 

Jupiter and his satellites as heavy bodies. — 
This planet is not only heavier, but its volume is much 
greater than that of any one of the planets. Being 5.2 
further from the sun than the earth, it will be attracted 
by a power diminished in the ratio of the square of 5.2 
to 1, or as 27 to 1 nearly. 

The weight of Jupiter is to that of the earth as 338 to 
1, and in case his diameter were exactly equal to that of 
the earth, a body weighing one pound at the terrestrial 
equator would weigh at the equator of this planet 338 
pounds. But the diameter of Jupiter is 90,734 miles, 
and its radius 45,377 miles, or more than ten times the 
radius of the earth. His attraction on a body upon the 
surface will therefore be reduced on account of this ten- 
fold distance to the one hundredth of 338 pounds, or to 
3.38 pounds, or, if the computation be made precisely, 
the result gives us 2.81 as the weight of one terrestrial 
pound at the equator of this planet. The student can 
compute the reduction in the gravity of the planet at the 
equator arising from the action of the centrifugal force, 
the planet revolving on its axis in 9h. 55m. 27s. 

The principal disturber of Jupiter is the planet Saturn. 



AS PONDERABLE BODIES. 345 

From the sun to Jupiter is 5.2, the earth's distance being 
1. From Jupiter to Saturn the distance is 4. 3 in the 
same terms. Hence, if Saturn weighed as much as the 
sun, his power over Jupiter would be greater in the ratio 
of (5.2) 2 to (4.3) 2 , or as 27.04 to 18.44, or as 1.47 to 1. 
But the sun weighs as much as 3,502 Saturns, and hence 
his power over Jupiter will exceed that of Saturn in the 
ratio of - 3 T 5 .!f to 1, or as 2,380 to 1. This, of course, 
is the ratio of the forces when the planets are in con- 
junction. When in opposition the interval between them 
is increased by the diameter of the orbit of Jupiter, or 
by 10.4, and thus it becomes 14.7, instead of 4.3, and 
in this position the disturbing power of Saturn is reduced 
in the ratio of (14.7) 2 to (4.3) 2 , or as 216.09 to 18.44, 
or as 12 to 1. 

We have already seen how we can ascertain the weight 
of this planet by observing the period of revolution of 
his satellites and by measuring their distances. By tak- 
ing these quantities from the table in the Appendix the 
student may compute readily the mass of Jupiter as com- 
pared with that of the earth. 

The eccentricity of the orbit of this planet amounts to 
0.0481, the semi-major axis being unity, or the distance 
from the center of the ellipse to the focus is equal 
to (242,500,000) x 0.0481=11,664,250 miles. This 
quantity is now slowly increasing, and gains every year 
in length 388 miles. This is due to the disturbing in- 
fluence of the surrounding planets, and after an immense 
period will reach a limit beyond which it cannot pass. 
The increment will then be converted into decrement, 
and a limit being again reached, the orbit in its figure 
thus oscillates between these limits in calculable, but (so 
far as I know) in periods not yet calculated. 

15* 



346 THE SUN AND PLANETS 

The same fact is true of the inclination of the plane 
of Jupiter's orbit to that of the ecliptic. On the 1st 
January, 1840, this inclination amounted to 1° 18' 42' / .4. 
Its present annual decrease is ".23, and should this con- 
tinue, at the end of about 200,000 years these planes 
would coincide. This, however, can never take place. 
The decrease finally comes to be converted into increase, 
and thus the plane of the orbit of Jupiter may be said to 
rock to and fro on the plane of the ecliptic in periods 
reaching to even millions of years. 

We have already noticed a source of perturbation in 
the case of Venus and the earth, arising from the ap- 
proximate commensurability of the periods of revolution 
of these planets. A like equation, as it is called, exists 
in the case of Jupiter and Saturn. Five periods of Jupi- 
ter are 21,663, and two of Saturn's periods are 21,519 
days ; so that in case the planets start at any given time 
from a conjunction, at the end of five revolutions of Jupi- 
ter and two of Saturn, the planets will return to nearly 
the same points of their orbits and to the same relative 
positions. But the synodical period, or the time from 
conjunction to conjunction of these planets is 7,253.4 
days, and three times this quantity amounts to 21,760.2. 
Hence we perceive Jupiter in this period will have per- 
formed five revolutions and 21,760—21,663 = 97 days 
over, while Saturn will describe two revolutions and 240 
days over, and during these excesses the planets advance 
in their respective orbits 8° 6'. Thus every third con- 
junction will fall 8° 6' in advance of the former one, and 
the conjunction line will be thus carried round the entire 
orbit in about 44 times x 21,760 days, or in 2,648 
years, at the end of which cycle the same exact condition 
will be restored, and all the perturbations in the same 



AS PONDERABLE BODIES. d4T 

time completely obliterated, provided the figures of the 
orbits remain unchanged. Indeed, a restoration is effected 
partially and almost completely in consequence of the 
triple conjunction which takes place in the period of 
21,760 days. These conjunctions fall at points on the 
orbits 120° apart, and thus tend to effect a restoration, 
which is only fully perfected, however, at the end of the 
great cycle of 2,648 years. 

Here we ( find again the cause which prevents the laws 
of Kepler from being rigorously applicable to the planet- 
ary movements. In case Jupiter existed alone, then the 
line drawn from the planet to the sun would sweep over 
equal areas in equal times, as it is carried by the planet 
around the sun. But the association of the two planets 
renders the application of this law no longer possible. 
Jupiter is dragged back by Saturn, and Saturn is dragged 
forward by Jupiter when they start off from their line 
of conjunction ; but here comes in a most wonderful 
compensation in the fact that whatever Jupiter's motion 
loses by the disturbing influence of Saturn, Saturn's mo- 
tion gains by the disturbing influence of Jupiter. So 
that the stun of the areas swept over by the lines joining 
the two planets with the sun will always be equal in 
equal times. 

We shall not extend further our notices of the results 
arising from the action of gravitation on the planets and 
their satellites — having discussed to some extent the 
mutual perturbations of Uranus and Neptune in a former 
chapter. 

We will close by an extension of the principle laid 
down in the case of Jupiter and Saturn to the entire 
planetary system. If at any moment lines were drawn 
from the center of the sun to each of the planets in the 



348 THE SUN AND PLANETS. 

entire system, and from the center of each of the planets 
to their respective satellites, the areas swept over by all 
these lines thus drawn will always be equal in equal 
times. Thus, while not a solitary planet or satellite can 
follow this law of equal areas, the combined scheme is 
bound by it in the most rigorous manner ; and if the 
amount of area described by the entire system in one 
hour were determined to-day, and be sent down to pos- 
terity, at the end of ten thousand years, a like computa- 
tion being made, the same identical result will be reached, 
provided the system remain free from any disturbing in- 
fluence exterior to itself. 

In case, therefore, the sun with all his planets and 
comets is, indeed, drifting through space into other stellar 
regions, the time may come when the fixed stars may so 
disturb the sum of the areas as to point out clearly the 
fact that our system has positively changed its location 
in space. 

We will close our discussion of the sun and his satel- 
lites by the examination of an hypothesis which has been 
propounded to account for the peculiar organization of 
this vast scheme of revolving worlds. 



CHAPTER XVI. 

THE NEBULAR HYPOTHESIS. 

The Arrangement of the Solar System.— The Phenomena for wnif!H 
Gravitation is Responsible. — The Phenomena Remaining to be Ac- 
counted for — Nebulous Matter as found in Comets. — Nebulous Mat- 
ter Possibly in the Heavens. — The Entire Solar System once a 
Globe of Neuulous Matter.— Motion of Rotation. — Radiation of 
Heat. — Condbnsation and its Effects. — Rings Disengaged from the 
Equator of the Revolving Mass. — Formation of Planets and of 
Satellites. 

In our examination of the scheme of worlds which re- 
volve around the sun we have found that the orbits of the 
planets are all nearly circular, that their planes are all 
nearly coincident with the plane of the ecliptic, and that 
this plane is nearly coincident with the plane of the sun's 
equator ; that the planets all revolve in the same direc- 
tion around the sun, and that the sun and planets and 
satellites all rotate on their axes in the same direction; 
that the periods of revolution grow shorter in the planets 
and satellites as their distances from their primary grows 
less ; that the sun rotates on his axis in a shorter period 
than that employed in the revolution of any planet; that 
every planet accompanied by satellites rotates on its axis 
in a less time than the period of revolution of any satel- 
lite. The law of gravitation is not responsible for any 
of these fads, and in ease we Compute the chances o\ siu-li 
an organization coming into being by accident, we shall 



350 THE NEBULAR HYPOTHESIS. 

find but one chance in so many millions that we are 
compelled to look to some higher cause than mere acci- 
dent to account for so great a multitude of combined 
phenomena. 

We have said that gravitation is not responsible for 
the facts above stated. In case a solitary planet be pro- 
jected with a given force, and in a given direction about 
the sun, and at a given distance, it will revolve, as we 
have seen, in one of four curves, and in any one of these 
curves it will be held equally by the law of gravitation. 
The plane in which it revolves may assume any angle 
with a fixed plane, the direction of the revolution may be 
the same or contrary to that in which the sun rotates, the 
orbit may be a circle, an ellipse, a parabola, or an hyper- 
bola, and yet the planet shall revolve, subject to the law 
of gravitation. It may rotate on its own axis either with 
or against its revolution in its orbit, and in case we give 
to this planet a satellite, the same statements are true 
with reference to this attendant. So that, so far as the 
law of gravitation is concerned, there might have been 
among the planets all the diversity in the form of their 
orbits in the angles of their inclination to a fixed plane, 
and in the direction of their motions, as are found among 
the comets, and yet each object would have been subject 
to the great law of universal gravitation. 

We cannot, therefore, affirm that the peculiar struc- 
ture of the solar system results from the laws of motion 
and gravitation, without pre-supposing a condition of 
matter entirely different from that now recognized as ex- 
isting in the planets and their satellites. We have already 
noticed the wonderful constitution of the comets. In 
these bodies is found a kind of matter which has been 
termed nebulous, in which the minute particles are sepa- 



THE NEBULAR HYPOTHESIS. 351 

rated by some repulsive force, and the entire mass is but 
a vapor of the most refined tenuity. 

Among the stellar regions the telescope has revealed 
objects whose light is so faint and whose forms are so ill 
defined that they have been regarded by many astrono- 
mers of high reputation to be analogous to the comets in 
their material, exhibiting the primitive or primordial con- 
dition of the matter composing the physical universe. 
This conjecture (for it is nothing more) may be true or 
false, but its truth or falsehood cannot in any way affect 
the credibility of the theory or hypothesis we are about 
to present. The present condition of matter cannot in 
any way be assumed to be the only condition in which it 
ever existed, since we now know it to be subject to extra- 
ordinary changes and most wonderful modifications. 

Let us, then, suppose that a time once was when the 
sun and all its planets and their satellites existed as one 
mighty globe of nebulous matter, whose diameter far ex- 
ceeded the present diameter of the orbit of Neptune, that 
to this stupendous globe a motion of rotation was given, 
and that its heat is slowly lost by radiation, and let us 
endeavor to follow the changes which must flow from the 
loss of heat and the operation of the laws of motion and 
gravitation, and learn whether from this parent mass a 
scheme of planets and satellites such as now exist can be 
generated. We prefer to present the reasoning in the 
language of M. Pontecoulent, one of the most eminent 
of the illustrious disciples of Newton — merely premising 
that in case the central rotating mass contracts by loss of 
heat that a time must come when, in consequence of the 
increased velocity of rotation, the force of gravity oi' a 
particle at the equator will be overcome by the centrifu- 
gal force generated by the velocity of rotation, and hence 



352 THE NEBULAR HYPOTHESIS. 

fiat zones or rings of vapor or nebulous matter must 
eventually be formed in the plane of the equator of the 
revolving globe : — 

" These zones must have begun by circulating round 
the sun in the form of concentric rings, the most volatile 
molecules of which have formed the superior part, and 
the most condensed the inferior part. If all the nebulous 
molecules of which these rings are composed had con- 
tinued to cool without disuniting, they would have ended 
by forming a liquid or solid ring. But the regular con- 
stitution which all parts of the ring would require for 
that, and which they would have needed to preserve 
whilst cooling, would make this phenomenon extremely 
rare. Accordingly the solar system presents only one 
instance of this, that of the rings of Saturn. Generally 
the ring must have broken into several parts, which have 
continued to circulate round the sun, and with almost 
equal velocity, while at the same time, in consequence of 
their separation, they would acquire a rotatory motion 
round their respective centers of gravity; and as the 
molecules of the superior part of the ring, that is to say, 
those furthest from the center of the sun, had necessarily 
an absolute velocity greater than the molecules of the in- 
ferior part which is nearest it, the rotatory motion, com- 
mon to all the fragments, must always have been in the 
same direction as the orbitual motion. 

•''However, if after their division one of these frag- 
ments has been sufficiently superior to the others to unite 
them to it by its attraction, they will have formed only a 
mass of vapor, which, by the continual friction of all its 
parts, must have assumed the form of a spheroid flattened 
at the poles and elongated in the direction of its equator. 
Here, then, are rings of vapor left by the successive re- 



THE NEBULAR HYPOTHESIS. 353 

treats of the atmosphere of the sun, changed into so many 
planets in the condition of vapor circulating round the 
sun, and possessing a rotatory motion in the direction of 
their revolution. This must have been the most common 
case ; but that in which the fragments of some ring would 
form several distinct planets possessing degrees of velo- 
city must also have taken place, and the telescopic plan- 
ets discovered during the present century seem to present 
an instance of this ; at least if it is not admitted with 
Olbers, that they are the fragments of a single planet, 
broken by a strong interior commotion. It is easy to 
imagine the successive changes produced by cooling on 
the planets whose formation has been just pointed out. 
Indeed, each of these planets, in the condition of vapor, 
is, in every respect, like one of the nebula in the first 
stage ; they must, therefore, before arriving at a state of 
solidity, pass through all the stages of change we have 
just traced in the sun. At first the condensation of their 
atmosphere will form round the center of the planet a 
body composed of layers of unequal density, the densest 
matter having, by its weight, approached the center, 
and the most volatile reached the surface, as we see in 
a vessel different liquids ranged one above another, ac- 
cording to their specific gravity to arrive at a state of 
equilibrium. The atmosphere of each planet will, like 
that of the sun, leave behind it zones of vapor, which will 
form one or several secondary planets, circulating round 
the principal planet as the moon does round the earth, 
and the satellites round Jupiter, Saturn, and Uranus, or 
else they will form, by cooling without dividing, a solid 
and continuous circle, of which we have an instance in 
the ring of Saturn. In every ease the direction of the 
rotatory and orbitual motion of the satellites or the ring 



354 THE NEBULAR HYPOTHESIS. 

will be the same as that of the rotatory motion of the 
planet; and this is completely confirmed by observation. 

"The wonderful coincidence of all the planetary mo- 
tions, (a phenomenon which we cannot, without infringing 
the laws of probability, regard as merely the effect of 
chance,) must then be the result even of the formation of 
the solar system on this ingenious hypothesis; we see 
also why the orbits of the planets and satellites are so 
little eccentric, and deviate so little from the plane of 
the solar equator. A perfect harmony between the 
density and temperature of their molecules in a state of 
vapor would have rendered the orbits rigorously circular 
and made to coincide with the plane of this equator ; but 
this regularity could not exist in all parts of such large 
masses ; there has resulted the slight eccentricities of the 
orbits of the planets and satellites, and their deviation 
from the plane of the solar equator. 

" When in the zones abandoned by the solar atmosphere 
there are found molecules too volatile either to unite with 
each other or with the planets, they must continue to 
revolve round the sun, without offering any sensible re- 
sistance to the motions of the planetary bodies, either on 
account of their extreme rarity, or because their motion 
is effected in the same way as that of the bodies they en- 
counter. These wandering molecules must thus present 
all the appearances of the zodiacal light. 

" We have seen that the figure of the heavenly bodies 
was the necessary result of their fluidity at the begin- 
ning of time. The singular phenomenon presented by 
the rigorous equality indicated by observation among the 
lesser motions of rotation and revolution of each satel- 
lite, an equality rendering the opposed hemisphere of the 
moon forever invisible to us, is another obvious conse- 



THE NEBULAR HYPOTHESIS. 355 

quence of this hypothesis. Indeed, supposing that the 
slightest difference had existed between the mean motion 
of rotation and revolution of our satellite while it was in 
the state of vapor or of fluidity, the attraction of the 
earth would have elongated the lunar spheroid in the 
direction of its axis towards the earth. The same attrac- 
tions would have tended to diminish insensibly the differ- 
ence between the rotatory and orbitual motions of the 
moon, so as to confine to narrow limits a condition 
sufficient to cause the axis of its equator, directed 
towards the earth, to be subject only to a species of 
periodical balancing constituting the phenomenon of libra- 
tion. If these oscillations are not now observed, it is be- 
cause they have ceased to exist in consequence of the 
resistance they have encountered in the course of time, 
even as the oscillations of the terrestrial axis in the in- 
terior of the earth, arising from the initial state of mo- 
tion, have been destroyed, and as indeed all the motions 
of the heavenly bodies have disappeared which have not 
had a permanent cause. 

" The principal phenomena of the planetary system 
are therefore explained with great facility by the hypo- 
thesis we are examining ; and as these successive changes 
of a nebulous mass and the leaving of a part of its 
substance by cooling, agree with all the leading pheno- 
mena, it must be allowed a high degree of probability. 
In this hypothesis the formation of the planets would not 
have been simultaneous ; they have been created succes- 
sively at intervals of ages ; the oldest are those which 
are furthest from the sun, and the satellites are of a 
more recent date than their respective planets. It may 
be, if we are ever permit ted to reach so high, that by 
an examination of the constitution of each planet WC may 



356 THE NEBULAR HYPOTHESIS. 

go back to the epoch of its formation, and assign to each 
its place in the chronology of the universe. It is like- 
wise seen that the velocity of the orbitual motion of each 
planet, as it is now, must differ little from that of the 
rotatory motion of the sun at the period when the planet 
was detached from its atmosphere. And as the rotatory 
motion is accelerated in proportion as the solar molecules 
are confined by cooling, so that the sum of the areas 
which they describe round the center of gravity would 
remain always the same, it follows revolutionary motion 
must be so much more rapid as the planet is nearer the 
sun, as is seen by observation. It likewise results that 
the duration of the rotation either of the sun or of a 
planet must be shorter than the duration of the nearest 
body which circulates round them ; this observation is 
completely confirmed even in those cases where the differ- 
ence between the duration of the two motions must be 
very slight. Thus the interior ring of Saturn being 
very close to the planet, the duration of its rotation must 
be almost equal, but a little longer than that of the 
planet. 

" The observations of Herschel give, indeed, 0.432 
as the duration of the rotation of the ring, and 0.427 as 
that of the planet ; why, then, should we not admit that 
this ring has been formed by the condensation of the at- 
mosphere of Saturn, which formerly extended to it? 
We may perhaps deduce from the laws of mechanics and 
the actual dimensions of the sun, and the known dura- 
tion of its rotation, the relation existing between the 
radius vector of its surface and the time of its rotation 
in the different stages of concentration through which it 
has passed. The third law of Kepler would be no 
longer the mere result of observation ; it would be di- 



THE NEBULAR HYPOTHESIS. 357 

rectly deduced from the primordial laws of the heavenly 
bodies. ; 

" In this system the particular form of the planets, 
the flattening at the poles, and bulging out at the equa- 
tor, is only the necessary consequence of the laws of the 
equilibrium of fluids, and easily explains the greater part 
of the phenomena observed by geologists in the consti- 
tution of the terrestrial globe, which appear inexplicable, 
if it is not admitted that the earth and planets have been 
originally fluid. 

" Let us now see what is the origin and part assigned 
to comets by this hypothesis. La Place supposes that 
they do not belong to the planetary system, and he re- 
gards them as masses of vapor formed by the agglomera- 
tion of the luminous matter diffused in all parts of the 
universe, and wandering by chance in the various solar 
systems. Comets would thus be, in relation to the plan- 
etary system, what the aerolites are in relation to the 
earth, with which they seem to have no original con- 
nection. When a comet approaches sufficiently near the 
regions of space occupied by our system to enter into the 
sphere of the sun's influence, the attraction of that 
luminary, combined with the velocity acquired by the 
comet, causes it to describe an elliptic or hjrperbolic 
orbit. But as the direction of this velocity is quite arbi- 
trary, comets must move in every direction and in every 
part of the sky. 

" The cometary orbits will, then, have every inclina- 
tion to the ecliptic ; and this hypothesis explains equally 
well the great eccentricity by which they are usually 
effected. Indeed, if the curves described by comets are 
ellipses, they must be greatly elongated, since their 
major axes are at least equal to the radius oi' the 



358 THE NEBULAR HYPOTHESIS. 

sphere of the sun's attraction ; and we must conse- 
quently be able to see only those whose eccentricity is 
very great, and perihelion distance inconsiderable ; all 
others, on account of their minuteness and distance, 
must always be invisible, unless at least the resistance 
of the ether, the attraction of the planets, or other un- 
known causes diminish their perihelion distance, and 
bring them nearer the terrestrial orbit. The same cir- 
cumstances may change the primitive orbits of some 
comets into ellipses, whose major axes are comparatively 
small ; and this has probably happened to the periodi- 
cal comets of 1759, 1819, and 1832. The laws of the 
curvilinear motion likewise show that the eccentricity 
of the orbit chiefly depends on the direction of the 
comet's motion on its entering the sphere of the sun's 
attraction ; and as this motion is possible in every di- 
rection, there are no limits to the eccentricities of the 
orbits of comets. 

" If, at the formation of the planets, some comets 
penetrated the atmospheres of the sun and planets, the 
resistance they met would gradually destroy their ve- 
locity ; they would then fall on those bodies describing 
spirals, and their fall would have the effect of causing 
the planes of the orbits and equators of the planets to 
remove from the plane of the solar equator. It is, 
therefore, partly to this cause, and partly to those we 
have developed above, that the slight deviations we now 
perceive must be attributed. 

" Such is a summary of the hypothesis of La Place on 
the origin of the solar system. This hypothesis ex- 
plains, in the most satisfactory manner, the three most 
remarkable phenomena presented by the planetary mo- 
tions. 



THE NEBULAE HYPOTHESIS. 359 

"1st The motion of the planets in the same direction, 
and nearly in the same plane. 

11 2d. The motion of the satellites in the same direction 
as their planets. 

' ' 3d. The singular coincidence in direction of the ro- 
tatory and orbitual motions of the planets and the sun, 
which in other systems would present inexplicable diffi- 
culties. 

" The no less remarkable phenomena of the smallness 
of the eccentricities and inclinations of the planetary 
orbits are also a necessary consequence of it, while we see 
at the same time why the orbits of the comets depart 
from this general law, and may be very eccentric, and 
have any inclination whatever to the ecliptic. The flat- 
tening of the form of the planets, shown on the earth by 
the enlargement of degrees of the meridian, and by the 
regular increase of weight in going from the equator to 
the poles, is only the result of the attraction of their mole- 
cules while they were yet in a state of vapor, combined 
with the centrifugal force produced by the rotatory mo- 
tion impressed on the fluid mass. In short, among the 
phenomena presented by the motions and the form of the 
heavenly bodies, there are none which cannot be ex- 
plained with extreme facility by the successive condensa- 
tion of the solar system ; and the more this system is 
examined the more we are led to acknowledge its proba- 
bility. 

" Undoubtedly, if, as La Place has himself said, a hy- 
pothesis not founded on observation or calculation must 
always be presented with extreme diffidence, this, it will 
be granted, acquires, at least by the union and agreement 
of so many different facts, all the marks of probability. 
But what, in my opinion, principally distinguishes it from 



360 THE NEBULAR HYPOTHESIS. 

the ordinary theories concerning the formation of systems, 
is the identity which it establishes between the solar sys- 
tem and the stars spread so profusely through the sky. 

" All the phenomena of nature are connected, all flow 
from a few simple and general laws, and the task of the 
man of genius consists in discovering those secret connec- 
tions, those unknown relations which connect the pheno- 
mena which appear to the vulgar to have no analogy. 
In going from a phenomenon of which the primitive law 
is easily perceived, to another in which particular cir- 
cumstances complicate it so as to conceal it from us, he 
sees them all flowing from the same source, and the 
secret of nature becomes his possession. Thus the laws 
of the elliptic motion of the planets led Newton to the 
great principle of universal gravitation, which he would 
have sought for in vain in the less simple phenomena of 
the rotatory motion of the earth, or the flux and reflux 
of the sea. But this great principle being once dis- 
covered, all the circumstances of the planetary motions 
were explained, even in their minutest details, and the 
stability of the solar system was itself only the necessary 
consequence of its conformation, without which, as New- 
ton thought, God would be constantly obliged to retouch 
his work, in order to render it secure. La Place, ex- 
tending to all the stars, and consequently to the sun, the 
mode of condensation by which the nebula are changed 
into stars, has connected the origin of the planetary sys- 
tem with the primordial laws of motion, without recur- 
ring to any hypothesis but that of attraction. He has, 
therefore, extended to the fixed stars the great law of 
universal gravitation, which is probably the only efficient 
principle of the creation of the physical world, as it is of 
its preservation." 



THE NEBULAR HYPOTHESIS. 861 

Such is a brief outline of one of the most sublime 
speculations that has ever resulted from the efforts of 
human thought. It carries us back to that grand epoch 
when '■ in the beginning God created the heavens and the 
earth," when matter was first called into being in its un- 
formed nebulous condition, and "the earth was without 
form and void," and darkness covered the might y deep 
of unfathomable space. But the Spirit of God moved on 
the boundless flood of vaporous matter scattered through 
the dark profound, and gave to each particle its now 
eternal function, impressed the laws of gravitation and 
motion, selected the grand centers about which the germs 
of suns and systems should form, and in infinite wisdom 
drew the plan of that one scheme which we have at- 
tempted to examine, among the millions that shine in 
splendor throughout the boundless empire of space. 



APPENDIX 



TABLES OF ELEMENTS. 

SOLAR ELEMENTS, EPOCH 1st JAN., 1801. 

Mean longitude 280° 39' 10".2 

Longitude of the perigee 270° 30' 05".0 

Greatest equation of center 1° 55' 27".3 

Decrease of same in one year 0".l73 

Inclination of axis to the ecliptic 82° 40' 00".0 

Motion in a mean solar day 7° 30' 00".0 

Motion of perigee in 365 days. . . 1' 01''.9 

Apparent diameter 32' 12".6 

Mean horizontal parallax 8". 6 

Rotation in mean solar hours ■ 607h 4Sm 0s 

Time of passing over one degree of mean longitude. . . . 24h 20m 58.1s 

Eccentricity of orbit (semi-axis major 1) 01685318 

Volume (earth as 1) 1415225 

Mass (earth as 1) 354936 

Mean distance in miles 95,000,000 

Same (earth's radius 1) 239S1 

Density (earth as 1). » 0.250 

Diameter in miles 8SS,646 

Gravity at equator 28.7 

In ono socond of time bodies fall in feet 4.62.0? 



ELEMENTS OF THE ORBIT OF MERCURY, EPOCH 1st JAN., 1801, 

Mean distanco from tho sun in miles 36,725,000 

Same (earth's distanoe as l) 387099 I 

Greatest distanco, same unit 466 

Least distance, same unit 30750 1 1 

Eccentricity (semi-axis major as l) 2056178 



364 APPENDIX. 

Annual variation of same (decrease) 0.000,000,03866 

Sidereal revolution in days 8*7.9692824 

Synodical revolution in days 115. 87? 

Longitude of perihelion at epoch 74° 57' 27".00 

Annual variation of same (increase) 5.81 

Longitude of ascending node 46° 23' 55".00 

Annual variation of same 10".07 

Inclination of orbit to ecliptic 7° 00' 13".30 

Annual variation of same 00". 18 

Mean daily motion in orbit 245' 32".6 

Time of rotation on axis 24h 05m 28s 

Inclination of axis to ecliptic Uncertain. 

Apparent diameter 6".69 

Diameter in miles 3089 

" (earth's being 1) 0.398 

Volume (earth's being 1) 0.0595 

Density (earth's being 1) 1.225 

Light received at perihelion (earth's being 1) 10.58 

Same at aphelion (earth's being 1) 4.59 

Weight of a terrestrial pound 0.48 

Space fallen through in one second of time, in feet 7.70 

Mass (earth's as 1) 0.0769 

ELEMENTS OP VENUS EOR THE 1st JAN., 1840. 

Mean distance from the sun in miles 68,713,500 

Same (earth's distance as 1) 7233317 

Greatest distance, same unit 7282636 

Least distance, same unit 7183998 

Eccentricity (semi-axis major as 1) 0068183 

Annual variation of same (decrease) 0000006271 

Sidereal revolution in days. 224.7007754 

Synodical revolution in days 583.920 

Longitude of the perihelion 124° 14' 25".6 

Annual variation of same (decrease) 3".24 

Longitude of the ascending node 75° 11' 29".8 

Annual variation of same (decrease) 20".50 

Inclination of orbit to the ecliptic 3° 23' 31".4 

Annual variation of same (increase) 0".07 

Mean daily motion in orbit 96' 7".8 

Time of rotation on axis 23h 21m 21s 

Inclination of axis to the ecliptic Uncertain 



APPENDIX. 365 

Apparent diameter 17".10 

Diameter in miles . r 1,896 

Diameter (earth's being 1) , 0.925 

Volume (earth's being 1) 9960 

Mass or weight (earth's being 1) « 894 

Density (earth's being 1) 0.923 

Light received at perihelion (earth's being 1) 1.94 

Same at aphelion (earth's being 1) 1. 91 

Weight of a terrestrial pound, or gravity 0.90 

Space fallen through in one second of time, in feet 14.5 



ELEMENTS OF THE EARTH, 1st JAN., 1801. 

Mean distance in miles 95,000,000 

Greatest distance (mean distance 1) 1.0167151 

Least distance, same unit 0.9832249 

Mean sidereal revolution (solar days) 365d 06h 09m 09s.6 

Mean tropical revolution 365d 05h 48m 49s.7 

Mean annualistic revolution 365d 06h 1 3m 49s.3 

Revolution of the sun's perigee (solar days) 7,645,793 

Mean Longitude (20" for aberration). 100° 39' 10".2 

Earth's motion in perihelio in a mean solar day. 1°01'09".9 

Mean motion in a solar day 0° 59' 08".33 

Mean motion in a sidereal day 0° 59' 58 '.64 

Motion in aphelion in a mean solar day 0° 57' 11". 50 

Mean longitude of perihelion 99° 30' 05 ".0 

Annual motion of perihelion (east) 1 1 ".3 

Same referred to the ecliptic 1' 01".9 

Complete tropical revolution of same in years 20, OS i 

Obliquity of the ecliptic 23° 27' 56 ".5 

Annual diminution of same. . . , .' "-457 

Nutation (semi-axis major) 9.4 

rrcccssion (annual) ; luni-solar. 50". 4 

[Procession in longitude 50 .1 

Complete revolution of vernal equinox in years 25,868 

Lunar nutation in longitudo 17 ".61 9 

Solar nutation in longitudo 1' . 1 ;>7 

Eccentricity of orbit (semi-axis major 1) 0.01678366 

Annual decrease 0.0000004 1 63 

Daily acceleration of sidereal over mean Bolai time 3' 66 .91 

From vernal equinox to summer solstice 92d 21h 60m 

From summer solstice to autumnal equinox 93d 13b 44m. 



366 APPENDIX. 

Erom autumnal equinox to winter solstice 89d 16h 44m 

From winter solstice to vernal equinox 89d Olh 33m 

Mass (sun as 1) 0.0000028173 

Density (water as 1) 5.6747 

Mean diameter in miles 7916 

Polar, " " 7898 

Equatorial " 7924 

Centrifugal force at equator 0.00346 

Light arrives from the sun in , 8' 13".3 

Aberration 20". 25 



ELEMENTS OF THE MOON.— EPOCH 1st JAN., 1801. 

Mean distance from the earth (earth's radius 1) 60.273433 

Mean sidereal revolution in days 27.321661 

Mean synodical revolution in days 29.5305887 

Eccentricity of orbit 0.054908070 

Mean revolution of nodes in days 6793.391080 

Mean revolution of apogee in days 3232.575343 

Mean longitude of node at epoch 13° 53' 17".7 

Mean longitude of perigee. 266° 10' 07".5 

Mean inclination of orbit 5° 08' 39".96 

Mean longitude of moon at epoch 118° 17' 08".3 

Mass (earth as 1) 0.011364 

Diameter in miles 2164.6 

Density (earth as 1) 0.556 

Gravity or weight of one terrestrial pound 0.16 

Bodies fall in one second, in feet 2.6 

Diameter (earth as 1) 0.264 

Density (water as 1) 3.37 

Inclination of axis 1° 30' 10".8 

Maximum evection 1° 20' 29".9 

" variation 35' 42".0 

" annual equation 11' 12".0 

" horizontal parallax 1° 01' 24".0 

Mean " " 57' 00".9 

Minimum " " 53' 48".0 

Maximum, apparent diameter 33' 31".l 

Mean " " 31' 07".0 

Minimum " " 29' 21".9 



APPENDIX. 867 



ELEMENTS OF MAES FOR THE 1st JAN., 1840. 

Mean distance from the sun in miles 145, 750,000 

Same (earth's distance as 1) 1.523691 

Greatest distance, same unit. 1 .6657195 

Least distance, same unit 1.3816025 

Eccentricity (semi-axis major as 1) 0932528 

Annual variation of same (increase) 0000090176 

Sidereal revolution in days 686.9794561 

Synodical revolution in days » 779.836 

Longitude of the perihelion 333° 6' 38".4 

Annual variation of same (increase) 15".46 

Longitude of the ascending node 48° 16' 18".0 

Annual variation of same (decrease) 25".22 

Inclination of orbit to the ecliptic 1° 51' 5". 7 

Annual variation of same (decrease) 0".01 

Mean daily motion in orbit. 31' 26".7 

Time of rotation on axis 24h 37m 22s 

Inclination of axis to the ecliptic 59° 41' 49" 

Apparent diameter. » 5".8 

Diameter in miles 4,07 

Diameter (earth's being 1) 0.519 

Volume (earth's being 1) 1364 

Mass or weight (earth's being 1) 0.134 

Density (earth's being 1) 0.948 

Light received at perihelion (earth's being 1) 524 

Same at aphelion (earth's being 1) 360 

"Woight of a terrestrial pound or gravity 0.49 

Space fallen through in one second of time, in feet 7.9 



868 



APPENDIX 




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370 APPENDIX 



ELEMENTS OF JUPITER FOR THE 1st JAN., 1540. 

Mean distance from the sun in miles 494,256,000 

Same (earth's distance as 1) 5.202767 

Greatest distance, same unit 5.453663 

Least distance, same unit 4.951871 

Eccentricity (semi-axis major as 1) .0482235 

Annual variation of same (increase) 000001593 

Sidereal revolution in days 4332.5848032 

Synodical revolution in days 398.867 

Longitude of the perihelion 11° 45' 32".8 

Annual variation of same (increase) 6". 65 

Longitude of the ascending node 98° 48' 37".8 

Annual variation of same (decrease) 15".90 

Inclination of orbit to the ecliptic 1° 18' 42".4 

Annual variation of same (decrease) 0".23 

Mean daily motion in orbit 4' 59".3 

Time of rotation on axis 9h 55m 26s 

Inclination of axis to the ecliptic. 86° 54' 30" 

Apparent diameter 38".4 

Diameter in miles 92,164 

Diameter (earth's being 1) 11.225 

Volume (earth's being 1) 1491. 

Mass or weight (earth's being 1) 342.738 

Density (earth's being 1) 0.238 

Light received at perihelion (earth's being 1) 0408 

Same at aphelion (earth's being 1) 0336 

"Weight of a terrestrial pound or gravity 2.45 

Space fallen through in one second of time in feet 39.4 



ELEMENTS OF JUPITER'S SATELLITES. 

No. 1. No Eccentricity. 

Sidereal revolution in days Id 18h 27m S3. 506s 

Mean distance (Jupiter's radius 1) 6.04853 

Inclination of orbit to a fixed plane 0° 00' 00".0 

Inclination of this plane to Jupiter's equator 0° 00' 06". 

Mass, that of Jupiter being 1,000,000,000 17328 

No. 2. No Eccentricity. 

Sidereal revolution in days 3d 13h 14m 36.393s 

Mean distance (Jupiter's radius 1) 9.62347 



APPENDIX 371 

Inclination of orbit to a fixed plane 0° 27' 50" 

, Inclination of this plane to Jupiter's equator 0° 01' 05" 

- /Retrograde revolution of nodes on fixed plane in years 29.9142 

Mass, Jupiter's being 1,000,000,000 25235 

No. 3. Eccentricity Small. 

Sidereal revolution in days 7d 03h 42m 33.362s 

Mean distance (Jupiter's radius 1) 15.35024 

Inclination of orbit to a fixed plane 0° 12' 20" 

Inclination of this plane to Jupiter's equator 0°05'02" 

Retrograde revolution of nodes on fixed plane in years 141.7390 

No. 4. Eccentricity Small. 

Sidereal revolution in days 16d 16h 31m 49.102s 

Mean distance (Jupiter's radius being 1) 26.99835 

Inclination of orbit to a fixed plane 0° 14' 58" 

Inclination of this plane to Jupiter's equator 0° 24' 04" 

Retrograde revolution of node on fixed plane in years. 531,000 



ELEMENTS OF SATURN FOR THE 1st JAN., 1840. 

Mean distance from the sun in miles 906,205,000 

Same (earth's distance as I) 9.5388 50 

Greatest distance, same unit 10.073278 

Least distance, same unit 9.004422 

Eccentricity (semi-axis major as 1) 05602G5 

Annual variation of same (decrease) 0.000003124 

Sidereal revolution in days 10759.2197106 

Synodical revolution in days 378.090 

Longitude of the perihelion 89° 54' 41".2 

Annual variation of same (increase) '. 19 ".31 

Longitude of the ascending node 112° 16' 34 .2 

Annual variation of same (decrease) 19".54 

Inclination of orbit to the ecliptic 2° 2 -J 29 .9 

Annual variation of samo (decrease) . 1 ,'» 

Mean daily motion in orbit 2' .6 

Time of rotation on axis 10b 29m 1 7s 

Inclination of axis to the ecliptic ". 81° 

Apparent diameter 17 .1 

Diameter in miles 75,070 

Diameter (earth's being 9.022 

Volume (earth's being 1) 7 7 2. 

Mass or weight (earth's being 1) 103.682 



372 APPENDIX. 

Density (earth's being 1) 0.138 

Light received at perihelion (earth's being 1) 0123 

Same at aphelion (earth's being 1) 0099 

Weight of a terrestrial pound or gravity 1.09 

Space fallen through in one second of time m feet 17.6 



ELEMENTS OF SATURN'S SATELLITES. 

No. 1. Mimas. 

Sidereal revolution in days Od 22h 37m 27. 9s 

Mean distance (Saturn's radius 1) 3.3607 

Epoch 1790.0 

Mean longitude at epoch 256° 58' 48" 

Eccentricity and Peri-Saturnium Unknown. 

No. 2. Enceladus. 

Sidereal revolution in days Id 08h 53m 06.7s 

Mean distance (Saturn's radius 1) 4.3125 

Epoch ■ 1836.0 

Mean longitude at epoch 67° 41' 36'' 

Eccentricity and Peri-Saturnium Unknown. 

No. 3. Tethts. 

Sidereal revolution in days Id 21h 18m 25.7s 

Mean distance (Saturn's radius 1) 5.3396 

Epoch 1836.0 

Mean longitude at epoch 313° 43' 48" 

Eccentricity and Peri-Saturnium Uncertain. 

No. 4. Dioxe. 

Sidereal revolution in days 2d 17h 41m OS. 9s 

Mean distance (Saturn's radius 1) 6.8393 

Epoch . 1836 

Mean longitude at epoch 327° 40' 48" 

Eccentricity and Peri-Saturnium Uncertain. 

No. 5. Rhea. 

Sidereal revolution in days 4d 12h 25m 10.8s 

Mean distance (Saturn's radius 1) 9.5528 

Epoch 1836.0 

Longitude at epoch 353° 44' 00" 

Eccentricity and Peri-Saturnium Uncertain. 

No. 6. Titan. 

Sidereal revolution 15d 22h41m 25.2s 

Mean distance (Saturn's radius 1) 22.1450 



APPENDIX. 373 

Epoch 1830.0 

Mean longitude at epoch 137° 21' 24" 

'-'. Eccentricity 0.02934 

" Longitude of Peri-Saturnium 256° 38' 11" 

No. 7. Hyperion. 

Sidereal revolution 21d 07h 07m 40.8s 

Mean distance (Saturn's radius 1) 26.7834 

Other elements unknown. 

Discovered (Sept. 19, 1848,) by Bond of Cambridge, and by 
Lassell, of Liverpool. 

No. 8. Japetus. 

Sidereal revolution 79d 7h 53m 40.4s 

Mean distance (Saturn's radius 1) 64.3590 

Epoch 1790.0 

Mean longitude at epoch 269° 37' 48" 

Eccentricity and Peri-Saturnium Unknown. 



ELEMENTS OP URANUS FOR THE 1st JAN., 1840. 

Mean distance from the sun in miles 1,822,328,000 

Same (earth's distance as 1) 19.18239 

Greatest distance, same unit 20.07630 

Least distance, same unit 18.28848 

Eccentricity (semi-axis major as 1) 0466006 

Annual variation of same Unknown. 

Sidereal revolution in days 30686.8205556 

Synodical revolution in days 369.656 

Longitude of the perihelion. 16S° 5 2 t" 

Annual variation of same (increase) 2".2S 

Longitude of the ascending node * 73° S 47 .8 

Annual variation of same (decrease) 30 .05 

Inclination of orbit to the ecliptic 0° 46 '29 '.2 

Annual variation of same (increase) .03 

Mean daily motion in orbit 42 .4 

Time of rotation on axis Unknown. 

Inclination of axis to the ecliptic Unknown. 

Apparent diameter 4 . I 

Diameter in miles 36,2 1 6 

Diameter (earth's being 1) 4.34 I 

Volume (earth's being L) 

Mass or weight (earth's being 1) L7.55] 



374 APPENDIX. 

Density (earth's being 1) 0.180 

Light received at perihelion (earth's being 1) 0027 

Same at aphelion (earth's being 1) 0025 

Weight of a terrestrial pound or gravity 0.76 

Space fallen through in one second of time, in feet 12.3 



ELEMENTS OF URANUS' SATELLITES. 

No. 1. Ariel. 

Sidereal revolution in days 2d 12h 29m 20.66s 

Mean distance 7.40 

No. 2. Ujibeiel. 

Sidereal revolution in days 4d 3h 28m 8.00s 

Mean distance 10.31 

No. 3. Titaxia. 

Sidereal revolution in days 8d 16h 56m 31.30s 

Mean distance 16.92 

No. 4. Oberon". 

Sidereal revolution in days 13d llh 7m 12.6s 

Mean distance 22.56 



ELEMENTS OF NEPTUNE FOR THE 1st JAN., 1854. 

Mean distance from the sun in miles 2,85°>,420,000 

Same (earth's distance as 1) 30.03627 

Greatest distance, same unit 30.29816 

Least distance, same unit 29.77438 

Eccentricity (semi-axis major as 1) 0087193 

Annual' variation of same Unknown. 

Sidereal revolution in days ; 60126.722 

Synodical revolution in days 3G7.488 

Longitude of the perihelion 47° 17' 58'' 

Annual variation of same Unknown. 

Longitude of the ascending node 130° 10' 12 ".3 

Annual variation of same Unknown. 

Inclination of orbit to the ecliptic , 1° 46' 59".0 

Annual variation of same Unknown 

Mean daily motion in orbit 21".6 

Time of rotation on axis ■. Unknown. 

Inclination of axis to the ecliptic Unknown. 



APPENDIX. 375 

Apparent diameter 2".4 

Diameter in miles 33,610 

Diameter (earth's being 1) 4.719 

Volume (earth's being 1) 76.6 

Mass or weight (earth's being 1) . . . . 19.145 

Density (earth's being 1) 0.222 

Light received at perihelion (earth's being 1) 0011 

Same at aphelion (earth's being 1) 0011 

"Weight of a terrestrial pound or gravity 1.36 

Space fallen through in one second of time, in feet 21.8 



No. 1. 



ELEMENTS OF NEPTUNE'S SATELLITES. 

Sidereal revolution 5d 2 lh 2m 43s 

Longitude of the ascending node 175° 40' 

Longitude of perihelion 177° 30' 

Inclination to ecliptic 151° 0' 

Eccentricity 0.10597 



ELEMENTS OF PERIODICAL COMETS. 

Hallet's Comet, 1835, Nov. 15. 

Time of perihelion passage 22h 41m 22s 

Longitude of perihelion 304° 31 ' 32" 

Longitude of the ascending node 55° 9' 59" 

Inclination to the ecliptic 17° 45' 5" 

The semi-axis 17.98796 

Eccentricity 0.96*739 1 

Period in days '27,8G5d.74 

Retrogrado 

Enokk's Comet, 1845, Aug. 9. 

Time of perihelion passage 15h llmlla 

Longitude of perihelion 1 ."> 7 ° 1 1 2] 

Longitude of the asoending node 33 i° 1 9 

Inclination to the ecliptic 13° Y 34" 

The semi-axis 2.21640 

Eccentricity 0.8 kl 136 

Period in days L,205d.23 

Direct 



376 APPENDIX. 

Biela's Comet, 1846, Feb. 11. 

Time of perihelion passage Oh 2m 503 

Longitude of perihelion 109° 5' 47" 

Longitude of the ascending node 245° 56' 58" 

Inclination to the ecliptic 12° 34' 14" 

The semi-axis 3.50182 

Eccentricity 0.755411 

Period in days 2,393d.52 

Direct 

Fate's Comet, 1843, Oct. 17. 

Time of perihelion passage 3h 42m 16s 

Longitude of perihelion 49° 34' 19" 

Longitude of the ascending node 209° 29' 19" 

Inclination to the ecliptic 11° 22' 31" 

The semi-axis 3.81179 

Eccentricity 0.555962 

Period in days 2,718d.26 

Direct 

De Vico's Comet, 1844, Sept. 2. 

Time of perihelion passage llh 36m 53s 

Longitude of perihelion 342° 31' 15" 

Longitude of the ascending node 63° 49' 31" 

Inclination to the ecliptic 2° 54' 45" 

The semi-axis 3.00946 

Eccentricity 0.617256 

Period in days l,993d.09 

Direct 

Brorsen's Comet, 1846, Feb. 25. . 

Time of perihelion passage 9h 13m 35s 

Longitude of perihelion 116° 28' 34" 

Longitude of the ascending node 102° 39' 36" 

Inclination to the ecliptic 30° 55' 7" 

The semi-axis 3.15021 

Eccentricity 0.793629 

Period in days 2,042d 24 

Direct 



* This comet which was observed double in 1846 was still divided at its return 
in 1852. 









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